Sure, let's find the volume of the given cylinder step by step.
1. Identify the given values:
- Height (\(\( h \)\)) of the cylinder = 13.6 cm
- Radius (\(\( r \)\)) of the base = 6.6 cm
2. Recall the formula for the volume of a cylinder:
The volume (\(\( V \)\)) of a cylinder is given by the formula:
\(\[
V = \pi r^2 h
\]\)
3. Substitute the given values into the formula:
- Substitute \(\( r = 6.6 \)\) cm and \(\( h = 13.6 \)\) cm into the formula.
4. Calculate the base area:
- The base area of the cylinder is \(\( \pi r^2 \)\). Substituting \(\( r = 6.6 \)\):
\(\[
\pi (6.6)^2
\]\)
- Evaluate \(\( (6.6)^2 \)\):
\(\[
(6.6)^2 = 43.56
\]\)
- Then the base area becomes:
\(\[
\pi \times 43.56
\]\)
5. Calculate the volume:
- Substitute \(\( \pi \times 43.56 \)\) and \(\( h = 13.6 \)\) into the volume formula:
\(\[
V = \pi \times 43.56 \times 13.6
\]\)
- Calculate the volume:
\(\[
V \approx 1861.1297534690505 \, \text{cm}^3
\]\)
6. Round the volume to the nearest tenth:
- To obtain the volume to the nearest tenth, look at the digit in the hundredths place.
- Since the digit in the hundredths place after 1861.1 is 2 (which is less than 5), we do not round up.
\(\[
V \approx 1861.1 \, \text{cm}^3
\]\)
Therefore, the volume of the cylinder is approximately 1861.1 cubic centimeters.
