Question

What is the volume of this cone?
height 19. Length 11.
Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.
___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 of the base,
- \( h \) is the height of the cone.

From your input, the height \( h \) is given as 19, but it's unclear what "Length 11" refers to. Since a cone has a radius \( r \) at the base, I will assume that "Length 11" refers to the diameter of the base of the cone.

To find the radius \( r \), you can divide the diameter by 2:

\[
r = \frac{d}{2} = \frac{11}{2} = 5.5
\]

Now that we have the radius and height, we can plug these values into the volume formula:

\[
V = \frac{1}{3} \pi (5.5)^2 (19)
\]

Calculating \( (5.5)^2 \):

\[
(5.5)^2 = 30.25
\]

Now substitute this back into the volume formula:

\[
V = \frac{1}{3} \pi (30.25) (19)
\]

Next, calculate \( 30.25 \times 19 \):

\[
30.25 \times 19 = 574.75
\]

Now substitute into the formula:

\[
V = \frac{1}{3} \pi (574.75)
\]

Now using \( \pi \approx 3.14 \):

\[
V \approx \frac{1}{3} (3.14) (574.75)
\]

First calculate \( 3.14 \times 574.75 \):

\[
3.14 \times 574.75 \approx 1805.4225
\]

Then divide by 3:

\[
V \approx \frac{1805.4225}{3} \approx 601.8075
\]

Finally, rounding to the nearest hundredth:

\[
V \approx 601.81 \text{ cubic millimeters}
\]

So the volume of the cone is approximately **601.81 cubic millimeters**.