Volume of a Sphere
Indu and Vallabh have a cubic box with a volume of 1,728 cubic inches. Their teacher, Ms. Sindur, tells them to find the volume of the largest ball that would fit inside of the box knowing that all the sides are equal as the box is a perfect cube. They try to find the volume but want to check their answer. Can you see if your answer matches theirs?
Use the approximation
The answer is 904.32.
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1 solution
Let's assume and justify the box is technically a cube as a ball is also just a sphere. Since we have a cube with a volume of 1, 728 inches, we know each side length has to be 12 inches. Once the largest ball that can fit slides in, we know the diameter has to be 12 because the ball is cramped inside. Then we know the radius is 6. Let's plug it in to the formula for finding a volume of a sphere. (4 times Pi times Radius Cubed) divided by 3. (4 times 3.14 times 6 Cubed) divided by 3. (4 times 3.14 times 216) divided by 3. 2712.96 divided by 3 gives us the answer.