Question

The figure below shows a cylindrical tank designed to hold chemicals. The tank is placed inside an open rectangular prism, which is designed to contain a spill if the tank leaks.

image

The tank has a diameter of 30 feet and is 20 feet in height.
The prism has a square base that is 40 feet along each side.
The volume of the tank and the volume of the prism are equal.
What is the approximate volume, in cubic feet, of the cylindrical tank?

What is the approximate height, in feet, of the rectangular prism?

Answer 1

Cylinder volume = πr^2h = π(15^2)(20) = 4500π ≈ 14,137.2 ft^3.

Prism height h = (cylinder volume)/(base area) = 4500π / (40^2) = (45/16)π ≈ 8.835 ft (≈ 8.84 ft).