What is the volume, in cubic inches, of a cone with a diameter of 6 inches and a height of 7 inches? Use 3.14 for pi. Round your answer to the nearest hundredth.(1 point)

cubic inches m

1 answer

To find the volume of a cone, you can use the formula:

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

Where:

  • \( V \) is the volume,
  • \( r \) is the radius, and
  • \( h \) is the height.

First, let's find the radius. The diameter of the cone is given as 6 inches, so the radius \( r \) is half of that:

\[ r = \frac{6}{2} = 3 \text{ inches} \]

The height \( h \) is given as 7 inches. Now, we can plug these values into the volume formula, using \( \pi \) as 3.14:

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

Calculating \( (3)^2 \):

\[ (3)^2 = 9 \]

Now substitute back into the formula:

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

Calculating \( 9 \times 7 \):

\[ 9 \times 7 = 63 \]

Now substitute that back in:

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

Calculating \( 3.14 \times 63 \):

\[ 3.14 \times 63 \approx 197.82 \]

Now divide by 3:

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

So, the volume of the cone is approximately:

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