Question

A cone-shaped pile of sawdust has a base diameter of 38 feet, and is 14 feet tall. Find the volume of the pile

Answer 1

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  $V = \frac{1}{3} B \cdot h$ = $\frac{1}{3} \pi r^2h$  ......[1]

,where B = $\pi r^2$

First find the radius(r);

Using Diameter(D) = 2r

38 =2r

Divide both side by 2 we get;

$\frac{38}{2} =\frac{2r}{2}$

Simplify:

19 = r

or r =19 feet

Now, substitute the value of r = 19 feet and h = 14 feet in [1]    [ Use value of  $\pi = \frac{22}{7}$ ]

then, we have:

$V = \frac{1}{3} \pi r^2h = \frac{1}{3} \cdot \frac{22}{7} \cdot (19)^2 \cdot (14)$

or

V = $=\frac{1}{3}\cdot 22 \cdot 19 \cdot 19 \cdot 2 = \frac{22 \cdot 19 \cdot 19 \cdot 2}{3}$

or

V = $\frac{15884}{3} =5,294.66667$ ≈ 5,294.67 cubic feet.

therefore, the volume of pile is; ≈ 5,294.67 cubic feet.