Sure! Let's work through the problem step by step.
1. Identify the given information:
- The height of the cylinder (h) is 14 cm.
- The diameter of the base is 6 cm.
2. Find the radius of the base:
- The radius (r) is half of the diameter.
- So, radius [tex]\( r = \frac{6}{2} \)[/tex] cm = 3 cm.
3. Recall the formula for the volume of a cylinder:
[tex]\[
V = \pi \cdot r^2 \cdot h
\][/tex]
Where:
- [tex]\( V \)[/tex] is the volume.
- [tex]\( r \)[/tex] is the radius of the base.
- [tex]\( h \)[/tex] is the height of the cylinder.
4. Substitute the known values into the formula:
[tex]\[
V = \pi \cdot (3 \text{ cm})^2 \cdot 14 \text{ cm}
\][/tex]
5. Calculate the volume:
- First, compute [tex]\( r^2 \)[/tex]: [tex]\( (3 \text{ cm})^2 = 9 \text{ cm}^2 \)[/tex].
- Next, multiply by the height: [tex]\( 9 \text{ cm}^2 \times 14 \text{ cm} = 126 \text{ cm}^3 \)[/tex].
- Finally, multiply by [tex]\( \pi \)[/tex] (approximately 3.14159):
[tex]\[
V = 3.14159 \times 126 \text{ cm}^3 \approx 395.84067435231395 \text{ cm}^3
\][/tex]
6. Round the volume to the nearest tenths place:
- The calculated volume is approximately 395.84067435231395 cm³.
- When rounded to the nearest tenth, this becomes 395.8 cm³.
Therefore, the volume of the cylinder is 395.8 cubic centimeters when rounded to the nearest tenths place.
