Question

A tank in the shape of a hemisphere has a radius of 4 feet. If the liquid that fills the tank has a density of 75 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?

Answer 1

The weight of the liquid can be found by multiplying its volume by its density. The volume will be that of a hemisphere, which can be found using the appropriate formula.

Hemisphere volume

The volume of a hemisphere with radius r is given by ...

`\sf V = \huge \text((2\pi)/(3)\huge \text)r^3`

When the radius is 4 ft, the volume is ...

`\sf V = \huge \text((2\pi)/(3)\huge \text)(4 \ ft)^3 = (128\pi )/(3) \ ft^3`

Weight

The weight of the liquid in the tank is found using the density.

`\sf W = \rho V`

`\sf W = (75 \ lb/ft^3)\huge \text((128\pi)/(3) \ ft^3\huge \text) = 3200\pi \ lb \thickapprox 10,053 \ lb`

The total weight of the liquid in the tank is about 10,053 pounds.