Question

What is the volume, in cubic millimeters, of the cone? The height is 12mm and the diameter is 14mm. Use 3.14 for pi. Round to the nearest hundredth.

Answer 1

To find the volume of a cone, we 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.

First, we need to determine the radius from the diameter. The diameter is given as 14 mm, so the radius \( r \) is:

\[
r = \frac{d}{2} = \frac{14}{2} = 7 \text{ mm}
\]

The height \( h \) is given as 12 mm.

Now we can substitute the values into the volume formula:

\[
V = \frac{1}{3} \cdot 3.14 \cdot (7^2) \cdot 12
\]

Calculating \( r^2 \):

\[
7^2 = 49
\]

Now substituting this back into the volume formula:

\[
V = \frac{1}{3} \cdot 3.14 \cdot 49 \cdot 12
\]

Calculating \( 49 \cdot 12 \):

\[
49 \cdot 12 = 588
\]

Now we substitute this value into the equation:

\[
V = \frac{1}{3} \cdot 3.14 \cdot 588
\]

Next, we multiply \( 3.14 \) by \( 588 \):

\[
3.14 \cdot 588 = 1847.92
\]

Now we divide by 3:

\[
V = \frac{1847.92}{3} \approx 615.9733333
\]

Rounding to the nearest hundredth, we get:

\[
V \approx 615.97
\]

Thus, the volume of the cone is approximately

\[
\boxed{615.97} \text{ cubic millimeters.}
\]