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 the coffee grounds the container can hold round ur answer to the nearest hundredth and use 3.14 for pi

Answer 1

The formula for the volume \( V \) of a cone is given by:

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

where
- \( r \) is the radius of the base of the cone, and
- \( h \) is the height of the cone.

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

Now, plug the values into the formula:

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

First, calculate \( r^2 \):

\[
r^2 = 3^2 = 9
\]

Now substitute \( r^2 \) back into the volume formula:

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

Next, calculate \( 9 \times 7 \):

\[
9 \times 7 = 63
\]

So now the equation becomes:

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

Now, calculate \( 3.14 \times 63 \):

\[
3.14 \times 63 = 197.82
\]

Finally, calculate \( \frac{1}{3} \times 197.82 \):

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

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

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