A right circular cylinder tank of height 1 foot and radius 1 foot is full of water. Taking the density of water to be a nice round 60 pounds per cubic foot, find the hydrostatic force in pounds on the side of the tank.
A)30 $\pi$
B)60
C)240 $\pi$
D)240
E)30
F)120 $\pi$
G)60 $\pi$
H)120

Question

A right circular cylinder tank of height 1 foot and radius 1 foot is full of water. Taking the density of water to be a nice round 60 pounds per cubic foot, find the hydrostatic force in pounds on the side of the tank.
A)30 $\pi$ 
B)60
C)240 $\pi$ 
D)240
E)30
F)120 $\pi$ 
G)60 $\pi$ 
H)120

Quizplus · Accepted Answer

The hydrostatic force on the side of the tank is calculated by integrating the pressure over the surface area. The pressure at a depth $ y $ is $ 60y $ (since pressure = density x depth). The force is the integral of pressure times the differential area, which results in $ 60 \pi \int_0^1 y \, dy = 60 \pi \left[ \frac{y^2}{2} \right]_0^1 = 30 \pi $.

A Right Circular Cylinder Tank of Height 1 Foot and Radius