Question

The volume of this cone is 376.8 cubic millimeters. What is the height of this cone?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

6 mm

h ≈
millimeters

Answer 1

To find the height of the cone, we can use the formula for the volume of a cone:

\[
V = \frac{1}{3} \pi r^2 h
\]

Where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height.

We are given:
- Volume \( V = 376.8 \) cubic millimeters,
- \( \pi \approx 3.14 \).

We also need to note that from the problem you provided, it seems like the radius is not mentioned. However, if you assume a radius (for example, given as 6 mm, or if that's assumed), you can then solve for the height. I'll proceed with using \( r = 6 \) mm.

First, let's plug in the values into the formula:

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

Calculating \( 6^2 \):

\[
6^2 = 36
\]

Now substitute this into the volume formula:

\[
376.8 = \frac{1}{3} \times 3.14 \times 36 \times h
\]

Calculating \( \frac{1}{3} \times 3.14 \times 36 \):

\[
\frac{1}{3} \times 3.14 \times 36 = \frac{113.04}{3} = 37.68
\]

Now the equation becomes:

\[
376.8 = 37.68h
\]

To solve for \( h \), divide both sides by \( 37.68 \):

\[
h = \frac{376.8}{37.68} \approx 10
\]

Rounded to the nearest hundredth, the height \( h \) is:

\[
h \approx 10.00 \text{ mm}
\]

Thus, the height of the cone is approximately **10.00 millimeters**. If the radius was something other than 6 mm, please provide that information for accurate calculations.