Question

You're uncle is having a new roof installed in his house. The roof is a square pyramid. The side length of the base of the roof is 28 foot. The volume of the roof is 18929.3333 cubic feet what is the height of the roof

Answer 1

The height of the roof in his house is 72.43 ft.

Explanation:

The volume of square pyramid is :

`V=\frac13 Bh`

B= area of the base.

h= the height.

Given that,

The roof is a square pyramid in shape. The volume of the roof is 18929.333 cubic feet.

The side length of the base of the roof is 28 feet.

Since the base of the roof is square in shape.

The area of the square is = side²

The area of the base is =(28×28) square feet

=784 square feet

Assume the height of the roof be h ft.

Then, the volume of the roof is =
`\frac13 Bh`

`=\frac13 * 784 * h` square feet.

According to the problem,

`\frac13 * 784 * h= 18929.3333`

`\Rightarrow h=(18929.3333* 3)/(28)`

`\Rightarrow h\approx 72.43` ft.

The height of the roof in his roof is 72.43 ft.