2005 iTest Problems/Problem 12

Problem

A sphere sits inside a cubic box, tangent on all $6$ sides of the box. If a side of the box is $5$ , and the volume of the sphere is $x\pi$ , find $x$ .

Solution 1

The diameter of the sphere is the same length as the side of the box, $5$ . Its radius is therefore $\frac{5}{2}$ . Plugging this radius into the formula for the volume of a sphere, our answer is $\frac{4}{3}\cdot2.5^3=\boxed{\frac{125}{6}}$ .

2005 iTest (Problems, Answer Key)
Preceded by: Problem 11	Followed by: Problem 13
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2005 iTest Problems/Problem 12

Problem

Solution 1

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