The Two Radii of the Frustum of a Right Circular $7,275 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }$

question 35

Multiple Choice

The two radii of the frustum of a right circular cone are increasing at a rate of 4 centimeters per minute, and the height is increasing at a rate of 12 centimeters per minute (see figure) . Find the rate at which the volume is changing when the two radii are 15 centimeters and 30 Centimeters, and the height is 10 centimeters.

• A) \(7,275 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }\)
• B) \(8,100 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }\)
• C) \(8,250 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }\)
• D) \(4,800 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }\)
• E) \(7,650 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }\)