Answer:
Given: Diameter of cone = 38 feet and height of cone = 14 feet.
Volume of cone V with radius r is one-third the area of the base B times the height h.
i,e [tex]V = \frac{1}{3} B \cdot h[/tex] = [tex]\frac{1}{3} \pi r^2h[/tex] ......[1]
,where B = [tex]\pi r^2[/tex]
First find the radius(r);
Using Diameter(D) = 2r
38 =2r
Divide both side by 2 we get;
[tex]\frac{38}{2} =\frac{2r}{2}[/tex]
Simplify:
19 = r
or r =19 feet
Now, substitute the value of r = 19 feet and h = 14 feet in [1] [ Use value of [tex]\pi = \frac{22}{7}[/tex] ]
then, we have:
[tex]V = \frac{1}{3} \pi r^2h = \frac{1}{3} \cdot \frac{22}{7} \cdot (19)^2 \cdot (14)[/tex]
or
V = [tex]=\frac{1}{3}\cdot 22 \cdot 19 \cdot 19 \cdot 2 = \frac{22 \cdot 19 \cdot 19 \cdot 2}{3}[/tex]
or
V = [tex]\frac{15884}{3} =5,294.66667[/tex] ≈ 5,294.67 cubic feet.
therefore, the volume of pile is; ≈ 5,294.67 cubic feet.
