A tank in the form of an inverted right circular cone is 8 meters across the top and 16 meters deep. The tank is filled with a liquid with the height of 8 meters weighing 950 kg/cu m. The work done, in Newton-meters, of pumping all the liquid out is

A) $104,000 \pi$
B) $\frac { 298,000 \pi } { 3 }$
C) $\frac { 11,916,800 \pi } { 3 }$
D) $\frac { 214,000 \pi } { 3 }$
E) $101,500 \pi$

Question

A tank in the form of an inverted right circular cone is 8 meters across the top and 16 meters deep. The tank is filled with a liquid with the height of 8 meters weighing 950 kg/cu m. The work done, in Newton-meters, of pumping all the liquid out is

A) $104,000 \pi$
B) $\frac { 298,000 \pi } { 3 }$
C) $\frac { 11,916,800 \pi } { 3 }$
D) $\frac { 214,000 \pi } { 3 }$
E) $101,500 \pi$

Quizplus · Accepted Answer

The work done is calculated by integrating the weight of each infinitesimal layer of liquid times the distance it needs to be lifted. The volume of a thin layer at height $ y $ is $\pi (4y/16)^2 \, dy$, and the weight is this volume times the density. Integrating from 0 to 8 meters gives the total work.

A Tank in the Form of an Inverted Right Circular 104,000π104,000 \pi104,000π

A Tank in the Form of an Inverted Right Circular $104,000 \pi$