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.
