Question

A rectangular prism and a cylinder both have a height of 8 m, and their cross-sectional areas are equal at every level parallel to their respective bases.

A rectangular prism and a cylinder both have a height of 8 meters. The rectangle has base dimensions of 5 meters by x. The cylinder has a radius of 3 meters.

Complete the steps to find the width of the prism.

Find the volume of the prism.
V =
m3
Find the volume of the cylinder.
V =
m3
Set the volumes equal to each other and solve for x. Round to the nearest tenth.
x =
m

Answer 1

Find the volume of the prism.
V = base area × height = (5x)·8 = 40x m^3

Find the volume of the cylinder.
V = πr^2h = π(3^2)·8 = 72π m^3

Set the volumes equal and solve for x.
40x = 72π ⇒ x = 72π/40 = (9π)/5 ≈ 5.7 m

x = 5.7 m (to the nearest tenth)