Question

Find the volume of the cone.
4 cm
12 cm
Question content area bottom
Part 1
The volume of the cone is approximately
  
enter your response here cubic cm.
​(Round to the nearest whole number as​ needed.)

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

From your question, it seems that:
- The radius \( r \) = 4 cm
- The height \( h \) = 12 cm

Now, substituting the values into the formula:

\[
V = \frac{1}{3} \pi (4 \text{ cm})^2 (12 \text{ cm})
\]

Calculating \( (4 \text{ cm})^2 \):

\[
(4 \text{ cm})^2 = 16 \text{ cm}^2
\]

Then, substituting that back into the volume formula:

\[
V = \frac{1}{3} \pi (16 \text{ cm}^2)(12 \text{ cm})
\]

Calculating further:

\[
V = \frac{1}{3} \pi (192 \text{ cm}^3)
\]

Now, multiply:

\[
V = \frac{192}{3} \pi \text{ cm}^3
\]
\[
V = 64\pi \text{ cm}^3
\]

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

\[
V \approx 64 \times 3.14 \text{ cm}^3 \approx 200.96 \text{ cm}^3
\]

Rounding to the nearest whole number:

\[
V \approx 201 \text{ cm}^3
\]

So, the volume of the cone is approximately **201 cubic cm**.