Question

A truck hauled 150 cubic feet of sand to a contraction site. The sand is dumped into a cone shaped pile 10 feet in height. What is the approximate diameter of the pile of sand

Answer 1

Diameter of pile of sand is 7.57 feet.

Explanation:

The volume of the cone =
`(1)/(3) (\pi ) r^(2) h`

Here, let π = 3.14,H = 10 ft, and V = 150 cubic feet.

So, putting the values in the formula, we get

`150 = (1)/(3) * 3.14 * r^(2) * 10`

or ,
`r^(2)  = (150 * 3 )/(3.14 * 10)`

or,
`r^(2)` = 14.33

or, r =
`√(14.33)`

⇒ r = 3.78 ft

As we know, 2 x RADIUS = DIAMETER

So, diameter of pile of sand = 2x 3.78= 7.57 feet.