Question

A cone has a radius of 5cm and a side of 9cm
What is the volume of the cone in cubic centimeters? Use 3.14 for pi. Round your answer to the nearest tenth.

Answer 1

To calculate the volume of a cone, we can use the formula:

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

where:
- \( V \) is the volume,
- \( r \) is the radius of the cone's base,
- \( h \) is the height of the cone, and
- \( \pi \) is approximately 3.14.

We are given:
- Radius \( r = 5 \) cm
- Slant height (side) = 9 cm.

To find the height \( h \) of the cone, we can use the Pythagorean theorem. The relationship involves the radius, height, and slant height as follows:

\[
s^2 = r^2 + h^2
\]

Where \( s \) is the slant height. Rearranging the equation for height \( h \) gives us:

\[
h^2 = s^2 - r^2
\]

Substituting the known values:

\[
s = 9 \, \text{cm}, \quad r = 5 \, \text{cm}
\]

Calculating \( h^2 \):

\[
h^2 = 9^2 - 5^2 = 81 - 25 = 56
\]

Now taking the square root to find \( h \):

\[
h = \sqrt{56} \approx 7.48 \, \text{cm}
\]

Now we can plug the values of \( r \) and \( h \) back into the volume formula:

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

Calculating \( r^2 \):

\[
r^2 = 5^2 = 25
\]

Now substituting the known values into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 25 \times 7.48
\]

Calculating the product:

1. Multiply \( 25 \times 7.48 = 186.96 \)
2. Then multiply by \( 3.14 \):
\[
3.14 \times 186.96 \approx 588.0144
\]
3. Finally, take one third of that:
\[
V \approx \frac{588.0144}{3} \approx 196.0048
\]

Rounding to the nearest tenth, we have:

\[
\boxed{196.0} \, \text{cubic centimeters}
\]