Question

A coffee maker has a cone shaped container that holds the coffee ground. The radius of the container is three inches and the height is seven 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 pi

Answer 1

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

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

where:
- \( r \) is the radius of the cone,
- \( h \) is the height of the cone,
- and \( \pi \) is approximately \( 3.14 \).

In this case, the radius \( r \) is 3 inches and the height \( h \) is 7 inches. Plugging in these values:

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

Now, calculate \( 3^2 \):

\[
3^2 = 9
\]

Then substitute back into the equation:

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

Calculate \( 9 \times 7 \):

\[
9 \times 7 = 63
\]

Now we substitute this back into the volume formula:

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

Now calculate \( 3.14 \times 63 \):

\[
3.14 \times 63 = 197.82
\]

Now divide by 3:

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

Rounding to the nearest hundredth, the volume of coffee grounds the container can hold is:

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