Let's calculate the volume of a cylinder with a given diameter and height step-by-step:
1. Convert Diameter to Radius and Unit Conversion:
- The diameter of the cylinder is given as 160 mm. To find the radius, we divide the diameter by 2.
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{160 \text{ mm}}{2} = 80 \text{ mm}
\][/tex]
- Convert the radius from millimeters to centimeters (since 1 cm = 10 mm).
[tex]\[
\text{Radius in cm} = \frac{80 \text{ mm}}{10} = 8 \text{ cm}
\][/tex]
2. Calculate the Volume of the Cylinder:
- The formula to calculate the volume [tex]\( V \)[/tex] of a cylinder is given by:
[tex]\[
V = \pi r^2 h
\][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.
- Substitute the radius and height into the formula. Here, [tex]\( r = 8 \text{ cm} \)[/tex] and [tex]\( h = 6 \text{ cm} \)[/tex].
[tex]\[
V = \pi (8 \text{ cm})^2 (6 \text{ cm})
\][/tex]
3. Compute the Volume:
- First, calculate the square of the radius:
[tex]\[
(8 \text{ cm})^2 = 64 \text{ cm}^2
\][/tex]
- Then, multiply this result by the height:
[tex]\[
64 \text{ cm}^2 \times 6 \text{ cm} = 384 \text{ cm}^3
\][/tex]
- Finally, multiply by [tex]\( \pi \)[/tex] (approximately 3.14159):
[tex]\[
V = \pi \times 384 \text{ cm}^3 \approx 3.14159 \times 384 \text{ cm}^3 \approx 1206.3715789784806 \text{ cm}^3
\][/tex]
4. Round the Volume to the Nearest Two Decimal Places:
- The calculated volume is approximately 1206.3715789784806 cm³.
- Rounding this to the nearest two decimal places, the volume is:
[tex]\[
\text{Volume} \approx 1206.37 \text{ cm}^3
\][/tex]
Thus, the volume of the cylinder is 1206.37 cm³ when rounded to the nearest two decimal places.
