Question

What is the volume of this cone?

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

6 mm
8.7 mm

cubic millimeters

Answer 1

To find 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, and \( h \) is the height of the cone.

In your case, the height \( h \) is given as 8.7 mm, and the diameter of the base is 6 mm. Therefore, the radius \( r \) is half of the diameter:

\[
r = \frac{6 \text{ mm}}{2} = 3 \text{ mm}
\]

Now, plug the values into the volume formula:

\[
V = \frac{1}{3} \pi (3 \text{ mm})^2 (8.7 \text{ mm})
\]

Calculating \( (3 \text{ mm})^2 \):

\[
(3 \text{ mm})^2 = 9 \text{ mm}^2
\]

Now substituting that back into the volume formula:

\[
V = \frac{1}{3} \pi (9 \text{ mm}^2) (8.7 \text{ mm})
\]

Calculating \( 9 \text{ mm}^2 \times 8.7 \text{ mm} \):

\[
9 \text{ mm}^2 \times 8.7 \text{ mm} = 78.3 \text{ mm}^3
\]

Now, substituting into the volume formula:

\[
V = \frac{1}{3} \pi (78.3 \text{ mm}^3)
\]

Using \( \pi \approx 3.14 \):

\[
V = \frac{1}{3} \times 3.14 \times 78.3 \text{ mm}^3
\]

Calculating \( 3.14 \times 78.3 \):

\[
3.14 \times 78.3 \approx 245.622
\]

Now divide by 3:

\[
V \approx \frac{245.622}{3} \approx 81.874
\]

Finally, rounding to the nearest hundredth:

\[
V \approx 81.87 \text{ cubic millimeters}
\]

Therefore, the volume of the cone is approximately **81.87 cubic millimeters**.