A trough whose cross-section is a trapezoid whose lower base is 4 feet long, upper base is 8 feet long, and is 4 feet high is filled with water of density 62.5 pounds per cubic foot. The force, in pounds, due to hydrostatic pressure on one end of the trough is

A) $3,000$
B) $\frac { 8,000 } { 3 }$
C) $2,250$
D) $1,000$
E)950

Question

A trough whose cross-section is a trapezoid whose lower base is 4 feet long, upper base is 8 feet long, and is 4 feet high is filled with water of density 62.5 pounds per cubic foot. The force, in pounds, due to hydrostatic pressure on one end of the trough is

A) $3,000$
B) $\frac { 8,000 } { 3 }$
C) $2,250$
D) $1,000$
E)950

Quizplus · Accepted Answer

The force due to hydrostatic pressure is calculated by integrating the pressure over the area of the trapezoidal end. The pressure at a depth $ y $ is $ 62.5y $. The area of a horizontal strip at depth $ y $ is $ \left(4 + \frac{y}{2}\right) \, dy $. Integrating from 0 to 4 feet gives the total force as $\frac{8,000}{3}$ pounds.

A Trough Whose Cross-Section Is a Trapezoid Whose Lower Base 3,0003,0003,000

A Trough Whose Cross-Section Is a Trapezoid Whose Lower Base $3,000$