Answer:
The approximate volume of dirt in the hill = 70372 ft³
Step-by-step explanation:
From the given information:
Laura uses a model of a truncated cone to estimate the volume of the dirt.
This implies that the volume of the dirt in the large hill took the shape of a truncated cone.
Her estimate then includes:
a base diameter = 80 feet ; then the base raidus (R) = 80 feet/2 = 40 feet
a top diameter = 40 feet ; then the top radius (r) = 40 feet/2 = 20 feet
a helght = 24 feet.
Using the formula for the volume of a truncated cone :
[tex]V =\dfrac{1}{3} \times \pi \times h \times ( r^2 +r \times R+ R^2)[/tex]
[tex]V =\dfrac{1}{3} \times \pi \times 24 \times ( 20^2 +20 \times 40+ 40^2)[/tex]
[tex]V =25.133 \times ( 400 +20 \times 40+ 1600)[/tex]
V = 70371.675 ft³
V ≅ 70372 ft³
