What is the volume of the cone 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 hundreth

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 of the base, and \(h\) is the height.

Given:

  • Diameter = 6 inches, so the radius \(r\) is half of the diameter: \[ r = \frac{6}{2} = 3 \text{ inches} \]
  • Height \(h = 7\) inches.

Now, plug the values into the volume formula using \(\pi \approx 3.14\):

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

Calculating \( (3)^2 \):

\[ (3)^2 = 9 \]

Now substituting it back into the volume formula:

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

Calculating \(9 \times 7\):

\[ 9 \times 7 = 63 \]

Now substitute again:

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

Calculating \(3.14 \times 63\):

\[ 3.14 \times 63 = 197.82 \]

Now divide by 3:

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

Thus, the volume of the cone to the nearest hundredth is

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