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Study Guide

A ball is a sphere. A sphere is a 3-D shape. 3-D shapes have volume. So a ball has volume. What it doesn't have is a base. So our tried and true formula for volume: Base × height, or* Bh*, doesn't work sp-here (get it?). Luckily, a brilliant ancient Greek mathematician named Archimedes figured out a formula for the volume of a sphere that doesn't require the area of a base. It is: 4/3 × pi × the radius cubed, or 4/3 π*r*^{3}.

Which came first, the circle or the sphere? They're eerily alike. A sphere has a center just like a circle does; it's the point in the middle of the sphere that is the same distance from every point on the sphere. A sphere has a diameter, just like a circle, and it goes from one point on the sphere, through the center, to another point on the sphere. And finally, just like a circle, the radius of a sphere is half the diameter. It's also the distance from the center to any point on the sphere.

If the radius of a sphere is 15 cm, then the volume is 4/3 (π) (15)^{3} which is 4/3 π (3375 cm^{3}) = 4500 π cm^{3} = 14,130 cm^{3}.

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