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 = [tex]\frac{1}{3} \pi r^{2} h[/tex]
Where [tex]\pi r^{2} = \text{Area of base }[/tex]
[tex]h= height[/tex]
So, volume of cone formed = [tex]\frac{1}{3}\times\text{Area of base}\times 9[/tex]
Since we know that amount of stone truck holds = Volume of cone formed
[tex]144=\frac{1}{3}\times\text{Area of circular base}\times 9[/tex]
[tex]144\times 3=\text{Area of base}\times 9[/tex]
[tex]432=\text{Area of circular base}\times 9[/tex]
[tex]\frac{432}{9}=\text{Area of circular base}[/tex]
[tex]48=\text{Area of circular base}[/tex]
Thus the area of the circular base is 48 square feet.
