Question

A tank in the shape of a hemisphere has a radius of 15 feet. If the liquid that fills the tank has a density of 97 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?​

Answer 1

685,653 lb

Explanation:

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 ...

V = (2π/3)r³

When the radius is 15 ft, the volume is ...

V = (2π/3)(15 ft)³ = 2250π ft³

Weight

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

W = ρV

W = (97 lb/ft³)(2250π ft³) = 218250π lb ≈ 685,653 lb

The total weight of the liquid in the tank is about 685,653 pounds.