Geometry

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# Surface Area of a Sphere

## Sphere Surface Area Formula

The formula for surface area of a sphere is given as:**SA = 4πr ^{2}**

Where

*SA*is the surface area and

*r*is the radius of the sphere.

### Example Problems

**Problem 1:**

Find the surface area of a sphere with a radius of 10.

Solution:

1.) Plugging what we know into the surface area formula, we get:

SA = 4πr^{2}

SA = 4π(10^{2}) = 400π

2.) **The surface area is 400π.**

**Problem 2:**

The surface area of a sphere is measured to be 100π square meters. What is the diameter of the sphere in meters?

Solution:

1.) First, we will plug the surface area value into the formula and solve for the radius *r*.

SA = 4πr^{2}

100π = 4πr^{2}

25 = r^{2}

r = 5

2.) Now that we have the radius, let’s convert it to diameter.

d = 2r

d = 2(5) = 10

3.) **The diameter of the sphere is 10 meters.**

Result :

Worksheet 1

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Cheat sheet

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