Question

A large dump truck will empty its full load of stone onto a small plot of land for storage. The rock forms a cone that is 9 feet tall. The truck holds 144 cubic feet of stone. What is the area of the circular base of the pile of stones?

Answer 1

Volume of a cone = (1/3) * Area of Base * height
144 * 3 / 9 = Area of Base
Area of the Base = 48

Answer 2

48 square feet.

Explanation:

A large dump truck will empty its full load of stone .

Those rock forms a cone.

Height of cone = 9 feet

The truck holds 144 cubic feet of stone.

So, amount of stone truck holds = Volume of cone

Formula of volume of cone =
`(1)/(3) \pi r^(2) h`

Where
`\pi r^(2) = \text{Area of base }`

`h= height`

So, volume of cone formed =
`(1)/(3)*\text{Area of base}* 9`

Since we know that amount of stone truck holds = Volume of cone formed

`144=(1)/(3)*\text{Area of circular base}* 9`

`144* 3=\text{Area of base}* 9`

`432=\text{Area of circular base}* 9`

`(432)/(9)=\text{Area of circular base}`

`48=\text{Area of circular base}`

Thus the area of the circular base is 48 square feet.