Kids Math

Finding the Volume and

Surface Area of a Sphere

**What is a sphere?**

A sphere is a three dimensional version of a circle, like a basketball or a marble. The definition of a sphere is "every point that is the same distance from a single point called the center."

**Terms of a Sphere**

In order to calculate the surface area and volume of a sphere we first need to understand a few terms:

Radius - The radius of a sphere is the distance from the center to the surface. It will be the same distance for a sphere no matter where it is measured from the surface.

Diameter - The diameter is a straight line from one point on the surface of the sphere to another that goes through the center of the sphere. The diameter is always twice the distance of the radius.

Pi - Pi is a special number used with circles and spheres. It goes on forever, but we will use an abbreviated version where Pi = 3.14. We also use the symbol π to refer to the number pi in formulas.

**Surface Area of a Sphere**

To find the surface area of a sphere we use a special formula. The answer to this formula will be in square units.

**Surface Area = 4πr**^{2}

This is the same as saying: 4 x 3.14 x radius x radius

**Example Problem**

What is the surface area of a sphere that has a radius of 5 inches?

4πr^{2}

= 4 x 3.14 x 5 inches x 5 inches

= 314 inches^{2}

**Volume of a Sphere**

There is another special formula for finding the volume of a sphere. The volume is how much space takes up the inside of a sphere. The answer to a volume question is always in cubic units.

Volume = 4/3 πr^{3}

This is the same as 4 ÷ 3 x 3.14 x radius x radius x radius

**Example Problem**

What is the volume of a sphere with a radius of 3 feet?

Volume = 4/3 πr^{3}

= 4 ÷ 3 x 3.14 x 3 x 3 x 3

= 113.04 feet^{3}

**Things to Remember**
- Surface area of sphere = 4πr
^{2}
- Volume of a sphere = 4/3 πr
^{3}
- You only need to know the radius to figure both the volume and surface area of a sphere.
- Answers for surface area problems should always be in square units.
- Answers for volume problems should always be in cubic units.

**More Geometry Subjects**

Circle

Polygons

Quadrilaterals

Triangles

Pythagorean Theorem

Perimeter

Slope

Surface Area

Volume of a Box or Cube

Volume and Surface Area of a Sphere

Volume and Surface Area of a Cylinder

Volume and Surface Area of a Cone

Angles glossary

Figures and Shapes glossary

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