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ruslelena [56]
3 years ago
7

A basketball id stored inside a cylindrical container as shown. The height of the cylinder is 8 inches and its radius is 4 inche

s. The radius of the basketball is 4 inches. What is the total volume in cubic inches of the space inside the cylinder that is unoccupied
Mathematics
1 answer:
german3 years ago
3 0

Answer:

134.041\ \text{in}^3

Step-by-step explanation:

r = Radius of sphere = Radius of basketball = 4 inches

h = Height of cylinder = 8 inches

Volume of unoccupied space will be the difference in volume between the cylinder and the basketball

\Delta V=\pi r^2h-\dfrac{4}{3}\pi r^3\\\Rightarrow \Delta V=\pi r^2(h-\dfrac{4}{3}r)\\\Rightarrow \Delta V=\pi\times 4^2(8-\dfrac{4}{3}\times 4)\\\Rightarrow \Delta V=134.041\ \text{in}^3

Unoccupied volume in the container is 134.041\ \text{in}^3.

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