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

Answer:

48 square feet.

Step-by-step 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 = $\frac{1}{3} \pi r^{2} h$

Where $\pi r^{2} = \text{Area of base }$

           $h= height$

So, volume of cone formed  = $\frac{1}{3}\times\text{Area of base}\times 9$

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

$144=\frac{1}{3}\times\text{Area of circular base}\times 9$

$144\times 3=\text{Area of base}\times 9$

$432=\text{Area of circular base}\times 9$

$\frac{432}{9}=\text{Area of circular base}$

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

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

Answer 2

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