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

𝜋
.(1 point)
cubic inches ,

1 answer

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 of the cone.

In this case, the radius \( r = 3 \) inches and the height \( h = 7 \) inches. Substituting these values into the formula:

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

First, calculate \( 3^2 \):

\[ 3^2 = 9 \]

Now substitute that back into the volume formula:

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

Now calculate \( 9 \times 7 \):

\[ 9 \times 7 = 63 \]

Then, substitute this into the formula:

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

Now calculate \( 3.14 \times 63 \):

\[ 3.14 \times 63 = 197.82 \]

Finally, divide this by 3 to find the volume:

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

Thus, the volume of the coffee grounds the container can hold is approximately

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