Question

Find the volume of a right circular cone that has a height of 19 e ft and a base with acircumference of 7.6 ft. Round your answer to the nearest tenth of a cubic foot

Answer 1

In order to solve this problem we will take in account the following picture and formula:

Where:

π ≅ 3.14159

h = height of the cone

r = radius of the base

V = volume

Now, our cone has the following dimensions:

h = 19 ft

c = circunference = 7.6 ft

We see that in order to obtain the volume we must replace the radius in the formula of the picture.

So we obtain first the radius r from the value of the circunference.

The circunference in terms of the radius is:

`c=2\pi r`

So the radius is:

`r=(c)/(2\pi)`

Now that we have the radius, we replace that in the formula for the volume:

`V=(1)/(3)\cdot\pi\cdot h\cdot r^2=(1)/(3)\cdot\pi\cdot h\cdot((c)/(2\pi))^2`

Now we replace the data of our right circular cone:

`\begin{gathered} V\cong(1)/(3)\cdot3.14159\cdot19ft\cdot((7.6ft)/(2\cdot3.14159))^2 \\ \cong29.1105ft^3 \\ \cong29.1ft^3 \end{gathered}`

So the volume of the right circular cone to the nearest tenth is: 29.1 ft³