Sure, let's find the volume of the given cylinder step by step.
1. Identify the given values:
- Height ([tex]\( h \)[/tex]) of the cylinder = 13.6 cm
- Radius ([tex]\( r \)[/tex]) of the base = 6.6 cm
2. Recall the formula for the volume of a cylinder:
The volume ([tex]\( V \)[/tex]) of a cylinder is given by the formula:
[tex]\[
V = \pi r^2 h
\][/tex]
3. Substitute the given values into the formula:
- Substitute [tex]\( r = 6.6 \)[/tex] cm and [tex]\( h = 13.6 \)[/tex] cm into the formula.
4. Calculate the base area:
- The base area of the cylinder is [tex]\( \pi r^2 \)[/tex]. Substituting [tex]\( r = 6.6 \)[/tex]:
[tex]\[
\pi (6.6)^2
\][/tex]
- Evaluate [tex]\( (6.6)^2 \)[/tex]:
[tex]\[
(6.6)^2 = 43.56
\][/tex]
- Then the base area becomes:
[tex]\[
\pi \times 43.56
\][/tex]
5. Calculate the volume:
- Substitute [tex]\( \pi \times 43.56 \)[/tex] and [tex]\( h = 13.6 \)[/tex] into the volume formula:
[tex]\[
V = \pi \times 43.56 \times 13.6
\][/tex]
- Calculate the volume:
[tex]\[
V \approx 1861.1297534690505 \, \text{cm}^3
\][/tex]
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.
[tex]\[
V \approx 1861.1 \, \text{cm}^3
\][/tex]
Therefore, the volume of the cylinder is approximately 1861.1 cubic centimeters.
