(5) A sphere has been placed inside a cylinder with the same dimensions; both have a radius of $6 cm$ , and a height of $12 cm$ . How many cubic centimeters of space does the sphere NOT fill up?
(A) $432 π {cm}^{3}$
(B) $72 π {cm}^{3}$
(C) $288 π {cm}^{3}$
(D) $144 π {cm}^{3}$

Answer

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Answer

Subtract the sphere volume from the cylinder volume: $V_{c y l i n d e r} - V_{s p h e r e} = 288 π {cm}^{3}$

Steps

Step 1 ：Find the volume of the cylinder: $V_{c y l i n d e r} = π r^{2} h = π (6)^{2} (12)$

Step 2 ：Find the volume of the sphere: $V_{s p h e r e} = \frac{4}{3} π r^{3} = \frac{4}{3} π (6)^{3}$

Step 3 ：Subtract the sphere volume from the cylinder volume: $V_{c y l i n d e r} - V_{s p h e r e} = 288 π {cm}^{3}$