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

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.

Given:

  • Radius \( r = 3 \) inches
  • Height \( h = 7 \) inches
  • \( \pi \approx 3.14 \)

Plugging in the values:

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

Calculating \( (3)^2 \):

\[ (3)^2 = 9 \]

Now substituting \( 9 \) into the volume formula:

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

Calculating \( 9 \times 7 \):

\[ 9 \times 7 = 63 \]

Now substituting \( 63 \) back into the formula:

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

Calculating \( 3.14 \times 63 \):

\[ 3.14 \times 63 \approx 197.82 \]

Now, finally dividing by 3:

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

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

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