Question

. What is the volume of the cone in terms of (pie) ifthe circumference of the base is 1.47 (pie) feet?

Answer 1

The circunference of a circle is given for the next formula:

$C=2\pi r$

Use the given circunference (1.4π ft) to find the radius (r):

$\begin{gathered} 1.4\pi ft=2\pi r \\ \\ r=\frac{1.4\pi ft}{2\pi} \\ \\ r=0.7ft \end{gathered}$

To find the volume use the next formula:

$V=\frac{h\cdot\pi\cdot r^2}{3}$

In the given cone you have:

radius (r) : 0.7ft

height (h) : 2.7ft

$\begin{gathered} V=\frac{2.7ft\cdot\pi\cdot(0.7ft)^2}{3} \\ \\ V=\frac{2.7ft\cdot\pi\cdot0.49ft^2}{3} \\ \\ V=0.441\pi ft^3 \end{gathered}$

Then, the volume of the cone is 0.441π cubic feet.

To find the volume of a cone you need to know the height and radius of the base. As you have the circunference of the base use that data to find the radius of the base knowing that the circunference is 2πr.

Then, you have a radius of the base of 0.7 ft and a height of 2.7ft. Use the formula of the volume of a cone (The volume of a cone is the product of height, radius and π divided into 3).

Then, the volume of the cone in terms of π is 0.441π cubic feet.