Surface area formula sphere Surface area formula The surface area, S, of a sphere with radius r is: S = 4πr 2 He also realized that the surface area of a sphere is exactly equal to the area of the curved wall of its circumscribed cylinder, which is the smallest cylinder that can contain the sphere. In this article, you will learn how to find the surface area of a sphere using the surface area of a sphere formula. Total surface area. Jun 11, 2023 · Learn how to calculate the surface area of a sphere using radius, diameter or circumference. Learn how to find its volume, surface area, radius, diameter, and circumference with formulas and examples We see surface area all the time in our everyday lives. Cube The surface area, S, of a cube with edge, s, is: S = 6s 2 Rectangular prism The surface area, S, of a rectangular prism is: S = 2lw + 2lh + 2wh where l is the length, w is the width, and h is the height of the rectangular prism. Surface area and volume are calculated using different formulas. Surface area calculator online - easyly calculate the surface area of a cube, rectangular prism, box, cylinder, sphere, cone, as well as triangular prism. We explain the formula for the area of a sphere = 4 × π × radius², and more. A "ball" is a sphere and everything inside the sphere. Area of the curved surface of a sphere is called the surface area of a sphere. What is the diameter of the sphere in meters? Solution: First, we will plug the surface area value into the formula and solve for the radius r. Solution We start by computing partial derivatives and find (13. Find the surface area of the sphere with radius a centered at the origin, whose top hemisphere has equation f (x, y) = a 2 x 2 y 2. 5. Given the radius r of the sphere, the total surface area is Nov 21, 2023 · Learn the formulas to calculate the surface area and volume of a sphere and why they might be needed. The calculations are done live: Aug 1, 2025 · Calculator online for a the surface area of a capsule, cone, conical frustum, cube, cylinder, hemisphere, square pyramid, rectangular prism, triangular prism, sphere, or spherical cap. The distance from the center of the sphere to any point on its surface is its radius. What is the ratio of their surface areas? Jun 22, 2023 · Surface Area of Sphere: Check here all about Sphere definition, solved problems, CSA, LSA and total surface area of sphere formula, units, examples, etc. the same distance) from a fixed point, called the centre or the origin of the sphere. It represents the total curved surface surrounding the sphere, and the factor 4π comes from integrating circular cross-sections over the sphere's surface area. Jul 23, 2025 · A sphere differs from a circle in the aspect that a circle is a two-dimensional (2D) shape, but a sphere is a three-dimensional (3D) shape. Online calculators and formulas for a hemisphere and other geometry problems. A sphere is a three-dimensional (3D Aug 1, 2025 · Calculator online for a sphere. Learn about the surface area of cylinder, cuboid, cube, cone, sphere, hemisphere, prisms with definitions, surface area formulas & solved examples from Cuemath. Aug 29, 2020 · This article provides formulas for the Surface Area and Volume of a Sphere and a Hemisphere with examples. If we integrate with respect to y and find the surface area between two vertical positions y1 and y2 we’d get exactly the same calculation. 2 adding up little strips of area. Our sphere area calculator makes your calculations much easier and quicker. Here, we will explore the different surface area formulas used to determine the total area of the outer surfaces of three-dimensional geometric shapes. You should also check out our spherical coordinates calculator and see how Our surface area of a hemisphere calculator is a handy tool that finds different types of hemisphere surface areas. Circular shapes take the shape of a sphere when observed as three-dimensional structures. The lateral area of any figure is the area of the non-base faces only. A sphere with radius r r has a volume of 4 3 π r 3 34πr3 and a surface area of 4 π r 2 4πr2. A Sphere is a having a round shape, just like a circle. All these formulas are mentioned in the table given below and an example is also provided here. This surface area calculator calculates the surface area of a sphere, cube, cylinder, pyramid, cone, and rectangular and triangular prism. Use formulas to find the surface area and volume of a sphere. Formulas Here are the key formulas for calculating a sphere's properties: Surface Area The surface area of a sphere is given by the formula $$ 4πr^2 $$ where r is the radius of the sphere. A sphere and a cylinder have the same radius, and the cylinder's height is equal to the sphere's diameter. What is a Sphere? As discussed in the introduction, the sphere is a geometrical figure that is round in shape. The surface area formula 4πr² arises from the geometric properties of a sphere and can be derived using calculus or geometry. Are you looking for an answer to the question of how to find the surface area of a hemisphere? Or maybe you just need to estimate it quickly? Whatever you plan to do, try this hemisphere calculator that comprises various area of a hemisphere formulas. Jun 11, 2025 · Learn how to calculate the area of a spherical surface using formulas and step-by-step methods for accurate geometric measurements. A sphere of radius r has surface area 4πr2. A sphere has several interesting properties, one of which is Jun 16, 2025 · Learn how to calculate the surface area of a sphere with formulas, solved examples, derivations, visuals, and real-life applications in this ultimate guide. How to Find the Volume of a Spherical Cap To find the volume of a spherical cap, substitute the values of the sphere radius ‘r’, and height of the spherical cap ‘h’, into the formula V = (πh2/3) (3r-h). The formula for it is given by (S) = 4πr2 4 π r 2, where ‘r’ is the radius of the circle. If we’re going to go to the e ort to complete the integral, the answer should be a nice one; one we can remember. Learn how to find the surface area of a hemisphere in terms of diameter. Learning surface area formulas helps in quickly solving the questions appearing on exams as well as practical applications like calculating material May 24, 2024 · Surface area and volume formulas help find dimensions of 3D figures like spheres and cylinders. The formula for the volume and Apr 9, 2025 · Calculate a hollow sphere's surface area using its inner and outer radii. Let us learn about the formula of surface area of a sphere and how to calculate the surface area of a sphere in this lesson. Calculate the surface area of a sphere easily! Online calculator for spherical surfaces. Sphere Calculations The calculator uses the following formulas to compute the volume, circumference, and area of a sphere: Volume of a sphere: V = ( 4/3 )πr3 Circumference of a sphere: C = 2πr Surface Area of a sphere: SA = 4πr2 Hemisphere Calculations A hemisphere is half of a sphere. It is perfectly symmetrical, and has no edges or vertices. Feb 16, 2025 · Discover the calculus behind a sphere’s surface area, 4πr², and explore its elegance with real-world applications in engineering, graphics, and physics. Nov 3, 2021 · Example 13 5 2: The surface area of a sphere. Learn more about the definition, formulas, and properties of the sphere in this article. A sphere’s surface area is the total area that the surface of the sphere covers, while its volume is the amount of space inside the sphere. Jun 25, 2017 · Get a list of shapes and their surface area formulas and volume formulas. Example: if you blow up a balloon it naturally forms a sphere because it is trying to hold as much air as possible with as small a surface as possible. Aug 1, 2025 · Calculator online for a capsule. Volume and surface area of a three-dimensional (3D) solid geometrical shape. The word "sphere" is from the Greek meaning "globe". Dec 2, 2018 · Some of you may have seen in school that the surface area of a sphere is 4 π R 2 4πR2, a suspiciously suggestive formula given that it’s a clean multiple of π R 2 πR2, the area of a circle with the same radius. [1] Discovered by the Greek philosopher and mathematician Aristotle thousands of years ago, the equation is relatively simple, even if its origins are not. Learn how to find the surface area of a sphere with stepwise formulas, solved examples, diagrams, and a handy calculator for quick answers. Additionally, the calculator will generate a step-by-step solution on how the problem was solved. See Surface area of a cylinder. Sphere calculator, formula, work with steps, step by step calculation, real world and practice problems to learn how to find the surface area and volume of sphere in inches, feet, meters, centimeters and millimeters. In this article, let us discuss how to derive the equation of a sphere along with the surface area and the volume of the sphere in detail. Just like a circle, each point of the sphere is at an equal distance from the center. approximately equal to 3. Simply input the Learn about the geometrical shape sphere and its real-life examples. Use our Surface Area Formula Calculator to find the surface area of 3D shapes like cubes, spheres, cones, and cylinders with ease. Find practical examples to understand these key geometric concepts easily. The formula of total surface area of a sphere in terms of pi (π) is given by: 3 days ago · A sphere is a perfectly round geometrical 3-dimensional object. r - radius of a sphere, V - volume of a sphere (sphere calc: find V), A - area of a sphere (sphere calc: find A), d - diameter of a sphere (sphere calc: find d), A / V - surface-to-volume ratio of a sphere. An interesting property of a sphere is that among all three-dimensional shapes with the same volume, it is the one with the minimum surface area. Aug 7, 2025 · Surface Area of Sphere = 4πr2 This formula shows that the surface area of a sphere is directly proportional to the square of its radius. The total surface area of the sphere is four times the area of great circle. Formula of Surface Area of Square A = 4πr2 where, r is the radius of the sphere and , π (pi) is a constant i. Learn the formula for calculating it, see examples, then test your math skills with a quiz. The sphere is defined in a three-dimensional space. Surface Area of a Sphere - Visual Explanation and Example is a lesson that will help you make sense of the formula for the surface area of a sphere. Oct 16, 2025 · The surface area of a sphere is the number of square units (cm 2, square inches, square feet -- whatever your measurement) that are covering the outside of a spherical object. Use our quick formulas, step-by-step guide & downloadable functions for geometry. 141 Sample Largest Volume for Smallest Surface Among all 3D shapes, the sphere encloses the most volume for the least surface area. We explain how to find the surface area of a sphere and provide a quick calculator to work it out for you, step-by-step. Of all shapes, a sphere has the smallest surface area for its volume. A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from the centre. SA = 4πr 2 100π = 4πr 2 25 = r 2 r = 5 Now that we have the radius, let's convert it to diameter. Hemisphere is a three-dimensional shape which is obtained when a sphere is cut along a plane passing through the center of the sphere. Surface area of a sphere is given by the formula: Surface Area of sphere = 4πr 2 where r is the radius of the sphere. Purpose: It aids in geometry education, engineering, and design by calculating surface areas for applications like material estimation, coating requirements, or structural analysis. As a dome-shaped section of a sphere, it shows the natural beauty of curved geometry and the constructive clarity of flat base surfaces. There is also a separate calculator which will find the radius and diameter of a sphere, if you already know the surface area. Simple formulas calculate the area and perimeter of 2D shapes like triangles and rectangles. Instead of memorizing complex formulas, this calculator automates the calculations for you. The surface area of a sphere formula is defined as the total area covered by its outer surface. Let us understand in detail about surface area formulas of different 3-D shapes. Hemispheres are created by Explore the formula to determine the surface area of a sphere and how to calculate it with step-by-step guidance and examples. Formulas of a Sphere There are four main formulas for a sphere which include sphere diameter formula, sphere surface area, and sphere volume. This calculator computes the surface area of a number of common shapes, including sphere, cone, cube, cylinder, capsule, cap, conical frustum, and more. [10] Another approach to obtaining the formula comes from the fact that it equals the derivative of the formula for the volume with respect to r because the total volume inside a sphere of radius r can be Surface Area Formulas The surface area formula is a mathematical solution to find the total area of any three-dimensional object occupied by all of its surfaces. Simple and clear steps included. Get important Facts by downloading the free PDF. This implies that the area of a sphere's curved surface must be utilized as the foundation rather than the contribution of its circular base to calculate its surface area. It's given by the formula Jul 23, 2025 · Learn how to calculate the volume and surface area of a sphere with simple formulas. Its mathematical properties - from the quadratic height dependence of volume to the linear cap surface - demonstrate the harmonic relationships of spherical geometry. This formula is derived from the fact that a sphere is made up of an infinite number of flat faces (or “patches”), each of which has an area equal to 4pir². Free surface area of a sphere GCSE maths revision guide, including step by step examples, exam questions and free worksheet. Aug 7, 2025 · And we can calculate the volume and the surface area of all of these objects by using relatively simple formulas. Let’s learn the formula, derivation with examples. Cube | Rectangular Prism | Prism | Sphere | Cylinder | Units A sphere is a three-dimensional shape or object that is round in shape. Example: Calculate the surface area of a The biggest circle of a sphere is a circle that has the same centre and radius of a sphere. Download and print the formulas for easy reference. The hemisphere can either be hollow or solid. Lateral area formulas help in calculating the lateral surface area of different figures including cuboid, cube, cylinder, cone, and sphere. Whether you are a student, engineer, architect, or simply someone working with measurements, this calculator makes it easy to compute surface area accurately. . A sphere is a set of points in three-dimensional space at the same distance from a given point, called the center. A sphere is a body bounded by a surface whose every point is equidistant (i. In this section, we will learn how to calculate the surface area and volume of the sphere. The distance from the center to the outer surface of sphere is called its radius. Some examples of spheres are a globe, football etc. A great circle of the sphere is a circle that has the same radius and centre as the sphere itself. Nov 1, 2025 · The surface area or total surface area of a 3-dimensional object is the measure of the total area of all its faces while the measure of the space occupied by a solid is called its volume. Calculate the unknown defining surface areas, height, base circumference, volumes and radii of a hemisphere with any one known variable. Jul 23, 2025 · The method for calculating surface area varies depending on the shape of the object. The surface area of a sphere can be found using the formula 4pir², where r is the radius of the sphere. After a visual explanation, we will use this Surface area is the total area covering the exterior of a shape. The surface of a sphere is perfectly round. Press the Play button to see. Calculate the surface areas, circumferences, volumes and radii of a sphere with any one known variables. Right cone Lateral Area Formula The lateral area formula is used to find the lateral area of any solid object. Aug 1, 2025 · Calculator online for a the surface area of a capsule, cone, conical frustum, cube, cylinder, hemisphere, square pyramid, rectangular prism, triangular prism, sphere, or spherical cap. Observe the figure given below to Jun 11, 2025 · Learn how to calculate the surface area of a sphere using the formula 4πr², where r is the radius of the sphere. It can be characterized as the set of all points located distance r r (radius) away from a given point (center). , objects with May 14, 2025 · The Surface Area Calculator is a tool that helps you determine the surface area of various 3D geometric shapes. In this example we will complete the calculation of the area of a surface of rotation. Volume of a Sphere Let’s tackle volume first. In other words, a sphere is a perfectly round geometrical object in three-dimensional space, just like a surface of a round ball. The area of a sphere is calculated by the formula S = 4πr². How to find the radius of a sphere? What's the radius of a sphere formula? Check out this radius of a sphere calculator and answer these questions. com Surface Area of Sphere The surface area of a sphere is the area occupied by the curved surface of the sphere. The sphere is three dimensional solid, that has surface area and volume. Note: A "sphere" is the outer surface of a "ball" (or "solid sphere"). What is a Surface Calculator? A Surface Calculator is a digital tool designed to calculate the surface area of different geometric figures. Calculate the unknown defining side lengths, circumferences, volumes or radii of a various geometric shapes with any 2 known variables. All we need to know is the radius of the sphere, which is the distance from the center of the sphere to any point on the surface of the sphere. However, if you want to learn about the area of the sphere formulas, keep reading. Unlike a cone, cube, or cylinder, a sphere has only one continuous surface (without an edges). To find the surface area of a sphere, use the formula (4πr 2 Free surface area of a sphere math topic guide, including step-by-step examples, free practice questions, teaching tips and more! The surface area of a sphere of radius r is: Archimedes first derived this formula [9] from the fact that the projection to the lateral surface of a circumscribed cylinder is area-preserving. For example, calculate the volume of the spherical cap with a sphere diameter of 10m and a spherical cap height of 3m. Let's learn more about the formula for the Surface Area of the Sphere with solved examples. A sphere has a surface area which is equal to 4πr^{2} square units. For this reason, spheres arise in a variety of physical systems where surface area is minimized, such as water droplets and soap bubbles! The surface area of a sphere can be calculated by means of the following formula. For example, if the radius of a sphere is doubled, its surface area increases by a factor of four. In other words, a hemisphere is half of a sphere. A sphere is a perfectly round solid figure. Welcome to our Area of a Sphere Calculator page. The surface area of a hemisphere is measured in square units. The Surface area of a sphere is the two-dimensional space that is occupied by the curved surface of the sphere. Learn to calculate the surface area of a sphere in Excel with ease. 3D solids like cubes, cylinders, cones, pyramids, and spheres. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i. In this guide, we go through all the formulas for calculating the surface area of a sphere, which is defined by on the radius, diameter, or circumference; with detailed explanations and examples for each method. Step-by-step methods and clear formulas explained for easy comprehension. An example is when a painting company is hired to paint the inside of a dome building. Utilizing the pyramid (or cone) volume formula of , where is the infinitesimal area of each pyramidal base (located on the surface of the sphere) and is the height of each pyramid from its base to its apex (at the center of the sphere). Online calculators and formulas for a surface area and other geometry problems. Surface area formula for solid cylinder, hollow cylinder, prism, cone, pyramid, sphere, hemisphere, cube, cuboid, rectangular prism and triangular prism, with video lessons with examples and step-by-step solutions. Aug 3, 2023 · What is a sphere with equations. See the derivation of the formula 4πr2 and solve problems with examples and diagrams. Learn how to calculate the volume, surface area, and other essential properties of spheres with solved examples. The surface area of a sphere is the measure of the region covered by the surface of a sphere. 3) f x (x, y) = x a 2 x 2 y 2 and f y (x, y) = y a 2 x 2 y 2 As our function f only defines the top upper hemisphere of the sphere, we double our What is the use of Finding the Surface Area of a Hemisphere? Other than being tasked directly with finding the surface area of a hemisphere (also called a semisphere or a half sphere), there are many real-world situations where our formula will be useful. Enter the radius, diameter, surface area or volume of a Sphere to find the other three. Surface body formulas and calculation examples. How to find the area of a sphere? If you only want to estimate its value, enter one of the chosen quantities into the right field. If we were to pop a basketball, or peel an orange, then lay them flat and measure the total area covered, the result would be their surface areas. For example, a globe or a soccer ball. The distance from the center to the surface is the radius. The surface area of a three-dimensional object is the total area of all its faces. Sphere: In geometry, a sphere is a 3D solid Geometric Shape formed by S Surface area of a sphere Use the Internet or some other resource to confi rm that the formula you wrote for the surface area of a sphere is correct. They need to know what the interior wall and floor Surface area formulas Many common objects have well-defined formulas for finding their surface areas. Example Problem 2 The surface area of a sphere is measured to be 100π square meters. Enter one value and get instant, accurate results. Note. The surface area of a sphere is defined as the amount Jul 23, 2025 · Sphere Formulas Some sphere formulas are added below, Surface Area of a Sphere The total surface of a sphere, including the curved surface, is the same in three dimensions. Surface area of sphere explained with pictures, examples and practice problems worked out. Nov 21, 2023 · Explore the surface area of a sphere in this 5-minute video. $$ 4 \cdot \pi r^2 $$ It can also be shown that the surface area of a sphere is equal to the lateral surface The sphere calculator finds the radius, diameter, surface area and volume of a sphere. Related Pages Surface Area of a Sphere A sphere is a solid in which all the points on the round surface are equidistant from a fixed point, known as the center of the sphere. The surface area of a hemisphere is the total area of all its faces. Note: Looking for the formula for the surface area of a sphere? Then check out this tutorial! You’ll see how to use a cylinder with the same dimensions to find the formula for the surface area of a sphere! May 14, 2025 · Calculate sphere volume, surface area, diameter, and more with this easy-to-use sphere calculator. It turns out that calculating the surface area of a sphere gives us just such an answer. A sphere's surface area is measured in square units. The surface area of a sphere is four times the area of its largest cross-sectional circle. The surface area of a sphere is defined as the region covered by its outer surface in three-dimensional space. How to calculate surface area of different 3D bodies. Remember that in an earlier example we computed the length of an in nites- imal segment of a circular A sphere is a three-dimensional round-shaped geometrical figure. See full list on basic-mathematics. All points on the surface of the shape are the same distance away from the centre – we call this distance the radius. With our area of a sphere calculator, you can analyze every parameter of a sphere you want, but it is chiefly dedicated to its surface area. This surface area calculator computes the surface area of common shapes, including sphere, cone, cylinder, torus, capsule, cube, rectangular prism, and conical frustum. d = 2r d = 2 (5) = 10 The diameter of the sphere is 10 meters. It supports both: 2D shapes like squares, rectangles, circles, triangles, etc. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. If you know the surface area By rearranging the above formula you can find the radius: r = √ The surface area of a sphere is the region or area covered by the outer, curved surface of the sphere. The surface area of a sphere is the area of that surface. Discover the sphere formula and its applications. Knowing measurements like radius or height helps apply formulas for both 2D and 3D shapes. Apr 9, 2025 · Calculate the surface area of a sphere precisely using proven formulas and reasoning, turning complex mathematics into simple engineering solutions. In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object. Online calculators and formulas for a sphere and other geometry problems. To know more about great circle, see properties of a sphere. e. iyna qnovz pujtlt fsrt tjfcxle uzkcmphw wygs pxq rmjlx twbcf xkgj iwumipuw hrlgs tzd drxknr