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)


(blank) cubic inches

1 answer

To find the volume of a cone, we 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.

  1. Calculate the radius: The diameter of the cone is 6 inches, so the radius \( r \) is: \[ r = \frac{6}{2} = 3 \text{ inches} \]

  2. Use the height: The height \( h \) is given as 7 inches.

  3. Substitute the values into the volume formula: Using \( \pi \approx 3.14 \): \[ V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7 \]

  4. Calculate \( (3)^2 \): \[ (3)^2 = 9 \]

  5. Substitute \( 9 \) into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]

  6. Calculate \( 9 \times 7 \): \[ 9 \times 7 = 63 \]

  7. Substitute \( 63 \) back into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 63 \]

  8. Calculate \( 3.14 \times 63 \): \[ 3.14 \times 63 = 197.82 \]

  9. Finally, divide by 3: \[ V = \frac{197.82}{3} \approx 65.94 \]

Thus, the volume of the cone is approximately:

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