Question

What number can be used to complete the volume statement for the cone below?

A cone with height 6 centimeters and Base 20.5 pi centimeters squared.

Volume =
Pi centimeters cubed

Answer 1

To find 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 of the base, and \( h \) is the height of the cone.

From the information given, the height \( h \) is 6 centimeters, and the base area is given as \( 20.5 \pi \) square centimeters. The base area of a cone can also be expressed as:

\[
\text{Base Area} = \pi r^2
\]

So we can set up the equation:

\[
\pi r^2 = 20.5 \pi
\]

Dividing both sides by \( \pi \):

\[
r^2 = 20.5
\]

Now we can find \( r \):

\[
r = \sqrt{20.5}
\]

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

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

Using \( r^2 = 20.5 \) and \( h = 6 \):

\[
V = \frac{1}{3} \pi (20.5)(6)
\]

Calculating this gives:

\[
V = \frac{1}{3} \pi (123) = 41 \pi
\]

Thus, the volume of the cone is:

\[
V = 41 \pi \text{ centimeters cubed}
\]

So the number that can be used to complete the volume statement is **41**.