Question

It is snowing and salt trucks are

dumping a mixture to help. When the
mixture is dumped from a truck, it
forms a mound with a conical shape. If
the mound has a diameter of 15 feet
and a height of 10 feet, how much
salt-sand mixture is there?

Answer 1

The volume of a mound of salt-sand mixture is 589.05 feet ³ or 589.05 cubic feet.

Explanation:

1. Let's check the information given to resolve the question:

Diameter of a mound of the mixture = 15 feet

Height (h) of the mound of the mixture = 10 feet

How much salt-sand mixture is there?

2. Let's find the volume of a mound of mixture with a conical shape:

For doing that, we need to use the volume formula of a cone.

It's: 1/3 * π * r² * h

Replacing with real values, we have:

1/3 * 3.1416 * 7.5 ² * 10 (Diameter = 15, so radius = Diameter/2 = 15/2 = 7.5)

Volume = 1/3 * 3.1416 * 56.25 * 10

Volume = 1/3 * 3.1416 * 562.5 (56.25 * 10 = 562.5)

Volume = 187.5 * 3.1416 = 589.05 feet ³ or 589.05 cubic feet.