Find the volume of a cone that has a base with a radius of 12 in. and has a height of 6 in. Let π=3.14

.(1 point)
Responses

452.16 in.2
452.16 in. squared

904.32 in.2
904.32 in. squared

2,712.96 in.2
2.712.96 in. squared

904.32 in.3

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,
  • \( h \) is the height of the cone,
  • \( \pi \) is a constant (which is given as 3.14).

Given:

  • \( r = 12 \) inches
  • \( h = 6 \) inches
  • \( \pi = 3.14 \)

Now, plug in the values into the formula:

\[ V = \frac{1}{3} \times 3.14 \times (12)^2 \times 6 \]

Calculate \( (12)^2 \):

\[ (12)^2 = 144 \]

Now substitute back into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times 144 \times 6 \]

Calculate \( 144 \times 6 \):

\[ 144 \times 6 = 864 \]

Now substitute that back:

\[ V = \frac{1}{3} \times 3.14 \times 864 \]

Now multiply \( 3.14 \times 864 \):

\[ 3.14 \times 864 \approx 2710.56 \]

Now take one-third of that:

\[ V \approx \frac{2710.56}{3} \approx 903.52 \]

Hence, the volume of the cone is approximately \( 904.32 \) cubic inches when rounded.

So the correct response is:

904.32 in.³