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Sphere – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">SphereSphere – Definition, ExamplesTable of ContentsUnderstanding Spheres in Mathematics Definition of Spheres

A sphere is a three-dimensional shape that is completely round with no edges. It is often referred to as the second cousin of a circle, but unlike a circle, it is a solid shape. Common examples of spheres in everyday life include playing balls, balloons, and light bulbs. What makes spheres unique among three-dimensional objects is that they have no flat surfaces, vertices, or edges, they only have a rolling surface, which distinguishes them from other 3D3D3D shapes like cubes, cones, and cylinders.

The sphere has several important elements that help us understand and work with it mathematically. The radius (rrr) is the distance from the center to any point on the sphere's surface. The diameter (ddd) is the longest straight line through the sphere, connecting two opposite points on the surface and passing through the center, calculated as d=2rd = 2rd=2r. The circumference is the greatest circular cross-section of the sphere, found using the formula C=2πrC = 2\pi rC=2πr. The surface area measures the total area of the sphere's outer surface and is calculated with SA=4πr2SA = 4\pi r^2SA=4πr2. The volume, which represents how much a hollow sphere can hold, is given by V=43πr3V = \frac{4}{3}\pi r^3V=34​πr3. sphere

Examples of Spheres Example 1: Finding the Circumference of a Sphere Problem:

If the radius of a sphere is 555 cm, find its circumference.

A circle with a radius of 5cm

Step-by-step solution:

Step 1, Write down the formula for the circumference of a sphere. The formula is C=2πrC = 2\pi rC=2πr, where rrr is the radius.

Step 2, Substitute the given radius value into the formula. We know that r=5r = 5r=5 cm, so we put this into our formula. C=2π×5C = 2\pi \times 5C=2π×5

Step 3, Calculate using the value of πππ as 3.143.143.14. C=2×3.14×5=31.4C = 2 \times 3.14 \times 5 = 31.4C=2×3.14×5=31.4 cm

Step 4, Write the final answer. The circumference of the given sphere is 31.431.431.4 cm.

Example 2: Calculating the Surface Area of a Sphere Problem:

If the radius of a sphere is 101010 cm, find its surface area.

A circle with a radius of 10cm

Step-by-step solution:

Step 1, Recall the formula for the surface area of a sphere. The formula is SA=4πr2SA = 4\pi r^2SA=4πr2, where rrr is the radius.

Step 2, Substitute the given radius value into the formula. We know that r=10r = 10r=10 cm. SA=4π×102SA = 4\pi \times 10^2SA=4π×102

Step 3, Simplify the expression by calculating the square of the radius. SA=4π×100SA = 4\pi \times 100SA=4π×100

Step 4, Calculate using the value of πππ as 3.143.143.14. SA=4×3.14×100=1,256SA = 4 \times 3.14 \times 100 = 1,256SA=4×3.14×100=1,256 cm²

Step 5, Write the final answer. The surface area of this sphere is 1,2561,2561,256 cm².

Example 3: Determining the Volume of a Sphere Problem:

What is the volume of a sphere of radius 777 cm?

A circle with a radius of 7cm

Step-by-step solution:

Step 1, Write down the formula for the volume of a sphere. The formula is V=43πr3V = \frac{4}{3}\pi r^3V=34​πr3, where rrr is the radius.

Step 2, Substitute the given radius value into the formula. We know that r=7r = 7r=7 cm.

V=43π×73V = \frac{4}{3}\pi \times 7^3V=34​π×73

Step 3, Calculate the cube of the radius.

V=43π×7×7×7=43π×343V = \frac{4}{3}\pi \times 7 \times 7 \times 7 = \frac{4}{3}\pi \times 343V=34​π×7×7×7=34​π×343

Step 4, Multiply all the values using πππ as 3.143.143.14.

V=43×3.14×343=1,436.02V = \frac{4}{3} \times 3.14 \times 343 = 1,436.02V=34​×3.14×343=1,436.02 cm³

Step 5, Write the final answer. The volume of the given sphere is 1,436.021,436.021,436.02 cm³.

Comments(6)FFashionistaLunaNovember 5, 2025This sphere glossary page is great! I've used it to help my students grasp sphere concepts. Clear defs and examples make learning a breeze.

SServerBobNovember 4, 2025This sphere glossary page is great! It helped my students grasp key concepts easily. Thanks for the clear explanations and examples!

BBookLover85September 17, 2025This page on spheres was super helpful for my kids! They finally got the concept of surface area and volume thanks to the clear examples. Loved the step-by-step solutions too!

NNatureLover92September 10, 2025I used the sphere definition and examples from this page to help my kids with their geometry homework. The step-by-step solutions made it super easy for them to understand 3D shapes!

NNatureLover25August 27, 2025This page was super helpful for explaining spheres to my kids! The examples and step-by-step solutions made it so easy for them to grasp the concepts. Thanks for keeping it simple and clear!

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