Question

Find the volume, in cubic inches, of a cone with a radius of 13 inches and a height of 27 inches. 

 


*Hint:  Don't forget to use your Desmos calculator and STAAR Reference Sheet to help!

Remember to use the  π
 symbol on your Desmos calculator.


(1 point)
Responses

4778.36 cubic inches
4778.36 cubic inches

176.98 cubic inches
176.98 cubic inches

14,335.09 cubic inches
14,335.09 cubic inches

1521 cubic inches

Answer 1

To find the volume \( V \) of a cone, you can use the formula:

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

where \( r \) is the radius and \( h \) is the height.

Given:
- Radius \( r = 13 \) inches
- Height \( h = 27 \) inches

Now, substitute the values into the formula:

\[
V = \frac{1}{3} \pi (13)^2 (27)
\]

Calculate \( (13)^2 \):

\[
(13)^2 = 169
\]

Now substitute back into the formula:

\[
V = \frac{1}{3} \pi (169) (27)
\]

Now multiply \( 169 \times 27 \):

\[
169 \times 27 = 4563
\]

Now substitute this value into the formula:

\[
V = \frac{1}{3} \pi (4563)
\]

Now divide by 3:

\[
\frac{4563}{3} = 1521
\]

Thus,

\[
V = 1521 \pi \text{ cubic inches}
\]

Using the approximate value of \( \pi \approx 3.14 \), we can find an approximate numerical value of the volume:

\[
V \approx 1521 \times 3.14 \approx 4778.34 \text{ cubic inches}
\]

So the volume of the cone is approximately \( 4778.36 \) cubic inches.

The correct answer from the provided responses is:

**4778.36 cubic inches**.