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

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 = (1)/(3) B \cdot h` =
`(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;

`(38)/(2) =(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 = (22)/(7)` ]

then, we have:

`V = (1)/(3) \pi r^2h = (1)/(3) \cdot  (22)/(7) \cdot (19)^2 \cdot (14)`

or

V =
`=(1)/(3)\cdot 22 \cdot 19 \cdot 19 \cdot  2 = (22 \cdot 19 \cdot 19 \cdot 2)/(3)`

or

V =
`(15884)/(3) =5,294.66667` ≈ 5,294.67 cubic feet.

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