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:
[tex]c=2\pi r[/tex]So the radius is:
[tex]r=\frac{c}{2\pi}[/tex]Now that we have the radius, we replace that in the formula for the volume:
[tex]V=\frac{1}{3}\cdot\pi\cdot h\cdot r^2=\frac{1}{3}\cdot\pi\cdot h\cdot(\frac{c}{2\pi})^2[/tex]Now we replace the data of our right circular cone:
[tex]\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}[/tex]So the volume of the right circular cone to the nearest tenth is: 29.1 ft³
