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:

$r=\frac{c}{2\pi}$

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

$V=\frac{1}{3}\cdot\pi\cdot h\cdot r^2=\frac{1}{3}\cdot\pi\cdot h\cdot(\frac{c}{2\pi})^2$

Now we replace the data of our right circular cone:

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

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