Question

Find the volume specified. Use 3.14 as the approximate value of pi​, and round your answer to the nearest tenth. Find the volume of a tent having the shape of a rectangular solid of length 14 ​ft, width 14 ​ft, and height 6 ft topped by a rectangular pyramid of the same width and length with height 5 ft.

Answer 1

The shape consists of rectangular solid and rectangular pyramid, so the volume of the shape is the sum of volumes of both solid and pyramid.

The volume of the rectangular solid is

`V_(solid)=\text{length}\cdot \text{width}\cdot \text{height}=14\cdot 14\cdot 6=1176\ ft^3.`

The volume of the pyramid is

`V_(pyramid)=(1)/(3)\cdot A_(base)\cdot \text{height}=(1)/(3)\cdot 14\cdot 14\cdot 5=(980)/(3)\ ft^3.`

Thus,

`V_(shape)=1176+(980)/(3)\approx 1502.7\ ft^3`

Answer: 1502.7 cubic feet

Answer 2

1502.7 cubic feet

Explanation:

We have a rectangular solid with the following dimensions:

length = 14 feet, width = 14 feet; and height = 6 feet.

We know that, volume of a rectangular solid = l x w x h

so putting in the given values to get:

volume of rectangular solid = 14 x 14 x 6 = 1176 cubic feet

We also have a rectangular pyramid with the following dimensions:

length = 14 feet, width = 14 feet; and height = 5 feet.

We know that, volume of a rectangular pyramid = (l x w x h) / 3

so putting in the given values to get:

volume of a rectangular pyramid = (14 x 14 x 5) / 3 = 326.7 cubic feet

Therefore, the volume of the tent = 1176 + 326.7 = 1502.7 cubic feet