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)

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 of the base of the cone,
  • \( h \) is the height of the cone,
  • \( \pi \) is approximately 3.14.

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

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

Calculating \( 3^2 \):

\[ 3^2 = 9 \]

Now substitute back into the formula:

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

Now calculate \( 9 \times 7 \):

\[ 9 \times 7 = 63 \]

Now substitute this back 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 by 3 to get the volume:

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

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

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