A town's public works department has ordered sand to spread on roadways during the upcoming winter snows. The delivered sand forms a right cone 36 feet high and a base diameter of 60 feet. How many cubic yards of sand has the department received?

Question

Mathematics

Mara Daugherty

26 November, 21:21

A town's public works department has ordered sand to spread on roadways during the upcoming winter snows. The delivered sand forms a right cone 36 feet high and a base diameter of 60 feet. How many cubic yards of sand has the department received?

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Answers (1)

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Lila Decker · Answer 1

1256 cubic yards of sand.

Step-by-step explanation:

In this question we have to find the volume of cone formed by sand.

Height of the cone is = 36 feet

Radius of the cone = 60/2 = 30 feet.

Now we know the formula of volume of cone v = π r² (h/3)

By putting the values of r and h we can get the volume of sand to spread.

Volume = π * (30) ² * (36/3) = 3.14*900*12 feet³

= 33912 feet³

Now we will convert feet³ to cubic yards

Since 1 cubic feet =.037037 cubic yards

therefore 33912 cubic feet = 33912*.037 = 1256 cubic yards.

So the answer is 1256 cubic yards of sand has the department received.