What is the volume of a cone with a diameter of 12 cm and a height of 11 cm? (1 point)

Responses

1,636.8 cubic centimeters
1,636.8 cubic centimeters

1,243.44 cubic centimeters
1,243.44 cubic centimeters

414.48 cubic centimeters
414.48 cubic centimeters

759.88 cubic centimeters

1 answer

To calculate 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,
  • \( h \) is the height,
  • \( \pi \) is approximately 3.14.

Given:

  • The diameter of the cone is 12 cm, so the radius \( r \) will be half of that: \[ r = \frac{12}{2} = 6 , \text{cm} \]
  • The height \( h \) is given as 11 cm.

Now, substituting the values into the volume formula:

\[ V = \frac{1}{3} \pi (6)^2 (11) \]

Calculating \( (6)^2 \):

\[ (6)^2 = 36 \]

Now substituting this value back into the formula:

\[ V = \frac{1}{3} \pi (36) (11) \] \[ V = \frac{1}{3} \pi (396) \]

Now calculating \( \frac{396}{3} \):

\[ \frac{396}{3} = 132 \]

So now we have:

\[ V = 132\pi \]

Using \( \pi \approx 3.14 \):

\[ V \approx 132 \times 3.14 \approx 414.48 , \text{cubic centimeters} \]

Thus, the volume of the cone is approximately 414.48 cubic centimeters.

The correct response is 414.48 cubic centimeters.