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Formula Volume of a Sphere

Sphere's Volume

Formula of sphere

Picture of Volume of Sphere

Example

sphere

The volume of the sphere pictured on the left is:

$$ v = \frac{4}{3} \pi r^3 \\ v = \frac{4}{3} \pi \cdot 3^3 \\ v = 36 \pi \\ = 113.1 \\ $$

Practice Problems

Problem 1

What is the surface area of a sphere with a radius of 7 in?

$$ v = \frac{4}{3} \pi r^3 \\ v = \frac{4}{3} \pi \cdot 7^3 \\ = 457.3 \text{ cubic inches} \\ $$

Problem 2

What is the surface area of a sphere with a diameter of 10 in?

First, remember that we need to divide the diameter by 2 to get the radius of 5 for our formula:

$$ v = \frac{4}{3} \pi r^3 \\ v = \frac{4}{3} \pi \cdot 5^3 \\ v = 36 \pi \\ = 523.6 \text{ cubic inches} \\ $$

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