Question

A coffee maker has a cone-shaped container to hold the coffee grounds. The radius of the container is 3 inches and the height is 7 inches. What is the volume, in cubic inches, of coffee grounds the container can hold? Round your answer to the nearest hundredth and use 3.14 for π.
.(1 point)
cubic inches

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, and \( h \) is the height.

Given:
- Radius \( r = 3 \) inches
- Height \( h = 7 \) inches
- \( \pi \approx 3.14 \)

Now, plug in the values into the formula:

\[
V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7
\]

Calculating \( (3)^2 \):

\[
(3)^2 = 9
\]

Now plug that back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 9 \times 7
\]

Now calculate \( 9 \times 7 \):

\[
9 \times 7 = 63
\]

Now we have:

\[
V = \frac{1}{3} \times 3.14 \times 63
\]

Calculating \( 3.14 \times 63 \):

\[
3.14 \times 63 \approx 197.82
\]

Now divide by 3:

\[
V = \frac{197.82}{3} \approx 65.94
\]

Therefore, the volume of the coffee grounds the container can hold is approximately:

\[
\boxed{65.94} \text{ cubic inches}
\]