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Formula Surface Area of a Sphere

Sphere's Surface Area

Picture of Volume of Sphere

Example

sphere

The surface area of the sphere pictured on the left is:

$$ A = 4\pi \cdot r^2 \\ A = 4\pi \cdot 3^2 \\ A = 36\pi \\ = 113.1 $$

Practice Problems

Problem 1

What is the surface area of a sphere with a diameter of 12 cm?

First, remember that we need to divide the diameter by 2 to get the radius of 6 for our formula:

$$ A = 4\pi \cdot 6^2 \\ A = 4\pi \cdot 6^2 \\ A = 144\pi \\ = 452.4 cm^2 $$

Problem 2

Find the radius of a sphere with a surface area of 196 $$\pi$ square inches?

Substitute the known values into the formula and solve for the radius.

$$ A = 4\pi \cdot r^2 \\ 196\pi = 4\pi \cdot r^2 \\ \frac{196\pi}{4\pi} = \frac{4\pi \cdot r^2}{4\pi} \\ 49 = r^2 \\ r^2 = \sqrt{49} = 7\text{ inches} $$

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