Sure, let's calculate the volume of a cylinder with the given dimensions step by step.
1. Convert the diameter from millimeters to centimeters:
- The diameter is given as 160 mm.
- Since there are 10 millimeters in a centimeter, we convert 160 mm to cm by dividing by 10:
[tex]\[
\text{Diameter in cm} = \frac{160 \text{ mm}}{10} = 16 \text{ cm}
\][/tex]
2. Calculate the radius of the cylinder:
- The radius is half the diameter.
[tex]\[
\text{Radius in cm} = \frac{\text{Diameter in cm}}{2} = \frac{16 \text{ cm}}{2} = 8 \text{ cm}
\][/tex]
3. Calculate the volume of the cylinder:
- The formula to find the volume of a cylinder is:
[tex]\[
V = \pi r^2 h
\][/tex]
Where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius, and [tex]\( h \)[/tex] is the height.
- Substitute the values [tex]\( r = 8 \text{ cm} \)[/tex] and [tex]\( h = 6 \text{ cm} \)[/tex] into the formula:
[tex]\[
V = \pi (8 \text{ cm})^2 \times 6 \text{ cm}
\][/tex]
- First, calculate the square of the radius:
[tex]\[
(8 \text{ cm})^2 = 64 \text{ cm}^2
\][/tex]
- Now multiply by the height:
[tex]\[
64 \text{ cm}^2 \times 6 \text{ cm} = 384 \text{ cm}^3
\][/tex]
- Finally, multiply by π (approximately 3.14159):
[tex]\[
V = 3.14159 \times 384 \text{ cm}^3 \approx 1206.3715789784806 \text{ cm}^3
\][/tex]
4. Round the volume to the nearest two decimal places:
- The volume rounded to two decimal places is:
[tex]\[
V \approx 1206.37 \text{ cm}^3
\][/tex]
Therefore, the volume of the cylinder is approximately 1206.37 cm³ when rounded to the nearest two decimal places.
