Question

The two cross sections shown are taken parallel to their respective bases. The cross sections have the same area. If the heights of the two solids are equal, find the volume of the cylinder. Round your answer to the nearest hundredth.

Answer 1

`489.40\,\,cm^3`

Explanation:

Given:

The given two cross-sections have the same area such that the heights of the two solids are equal.

To find: volume of the cylinder

Solution:

Let r represents the radius of the cylinder.

Area of the cross-section of the cylinder ( i.e., area of a circle) = area of the cross-section of the other solid (are of the rectangle)

`\pi r^2 =3.8* 8.1\\r^2=(3.8* 8.1)/(\pi)`

Height of the cylinder (h) = 15.9 cm

Volume of the cylinder
`=\pi r^2 h`

`=(\pi)(3.8* 8.1)/(\pi)(15.9)`

`3.8* 8.1* 15.9=489.40\,\,cm^3`