Question

In cold climate areas, trucks are used to disperse salt on the roads in order to de-ice the roads, making them safe for travel. In some cases, cone- shaped sheds store the salt during the off-season, or until the roads need to be de-iced. This large salt storage shed sits 12 feet above the ground and holds approximately 51.4 cubic feet of salt. To the nearest hundredth of a foot, what is the radius of the large storage shed? Use 3.14 for . In your final answer, include all of your calculations.

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Answer 1

We have been given that the shape of the storage shed is in the form of Cone.

It has been given that the shed sits 12 feet above the ground and it holds 51.4 cubic feet of salt.

So basically we've been given:

Height
`=h=12 ft`

Volume
`=51.4 ft^3`

So using the formula for the volume of cone, we get:

`V=(1)/(3) \pi r^2 h`, where 'h' is the height of the cone, V is the volume, and 'r' is the radius of the cone.

Plugging the values of height and volume in the equation we get:

`51.4=(1)/(3) \pi r^2(12)`

Solving for 'r', we get:

`r^2=(3 * 51.4)/(12*\pi)=4.092`

`r^2=4.092`

`r=√(4.092)=2.02`

Therefore, the radius of the cone is 2.02 or 2 feet.