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

First, we need to find the cross-sectional area of each figure:

• Cross-sectional area of the rectangular prism: 5x square meters
• Cross-sectional area of the cylinder: π(3^2) = 9π square meters

Since the cross-sectional areas are equal at every level, we can set up the following equation:

5x = 9π

Solving for x, we get:

x = 9π/5

Now, we can find the volume of the rectangular prism:

V = 5x * 8 = 72π cubic meters

And the volume of the cylinder:

V = π(3^2) * 8 = 72π cubic meters

Since the volumes are equal, we can set up the following equation:

72π = 72π

Simplifying, we get:

9πx = 40π

Solving for x, we get:

x = 40/9

Rounding to the nearest tenth, we get:

x ≈ 4.4 meters

Therefore, the width of the rectangular prism is approximately 4.4 meters.