Question

A cone has a height of 9 inches and a diameter of 4 inches. Calculate the volume of the cone

Answer 1

To calculate the volume of a cone, you can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cone.

Given:
- Height \( h = 9 \) inches
- Diameter \( d = 4 \) inches

First, we need to find the radius \( r \):

\[
r = \frac{d}{2} = \frac{4}{2} = 2 \text{ inches}
\]

Now we can substitute \( r \) and \( h \) into the volume formula:

\[
V = \frac{1}{3} \pi (2)^2 (9)
\]

Calculating the expression:

\[
V = \frac{1}{3} \pi (4)(9) = \frac{1}{3} \pi (36) = 12\pi
\]

Now, if you want to express the volume in terms of numerical value, using \( \pi \approx 3.14 \):

\[
V \approx 12 \times 3.14 \approx 37.68 \text{ cubic inches}
\]

Thus, the volume of the cone is \( 12\pi \) cubic inches, or approximately \( 37.68 \) cubic inches.