Question

2 points

The tent pictured below can be modeled as a rectangular prism with a
half-cylinder on top. The rectangular prism is 20 feet wide, 12 feet high,
and 45 feet long. The half-cylinder has a diameter of 20 feet. To the
nearest cubic foot, what is the volume of the tent?
20 ft
12 ft
ООО
39,074
17.869
24,937
67,349

Answer 1

Given:

Width of rectangular prism = 20 ft

height of rectangular prism = 12 ft

Length of rectangular prism = 45 ft

Cylindrical diameter = 20 ft

To find:

Volume of the tent

Solution:

Volume of the rectangular prism = length × width × height

= 45 × 20 × 12

Volume of the rectangular prism = 10800 ft³

Radius of cylinder = 20 ÷ 2 = 10 ft

Height of cylinder = length of rectangular prism

Volume of cylinder =
`\pi r^(2) h`

Volume of half cylinder =
`(1)/(2) \pi r^2h`

`$=(1)/(2) * 3.142* 10^2 *45`

Volume of half cylinder = 7069.5 ft³

Volume of tent = volume of rectangular prism + volume of half cylinder

= 10800 ft³ + 7069.5 ft³

= 17869.5 ft³

= 17869 ft³ (nearest cubic foot)

The volume of the tent is 17869 cubic feet.