Sure! Let's calculate the volume of a cylinder with the given dimensions step-by-step.
1. Convert the diameter to centimeters:
- Given diameter = 160 mm.
- Since 1 cm = 10 mm, we convert the diameter from mm to cm:
[tex]\[
\text{Diameter (cm)} = 160 \, \text{mm} \times \frac{1 \, \text{cm}}{10 \, \text{mm}} = 16 \, \text{cm}
\][/tex]
2. Find the radius:
- The radius is half of the diameter.
[tex]\[
\text{Radius (cm)} = \frac{\text{Diameter (cm)}}{2} = \frac{16 \, \text{cm}}{2} = 8 \, \text{cm}
\][/tex]
3. Calculate the volume of the cylinder:
- The formula for 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
- [tex]\(h\)[/tex] is the height
- We substitute the radius [tex]\(r = 8 \, \text{cm}\)[/tex] and the height [tex]\(h = 6 \, \text{cm}\)[/tex] into the formula:
[tex]\[
V = \pi (8 \, \text{cm})^2 \times 6 \, \text{cm}
\][/tex]
4. Compute the volume:
- First, calculate the area of the base:
[tex]\[
\pi (8 \, \text{cm})^2 = \pi \times 64 \, \text{cm}^2 \approx 201.06 \, \text{cm}^2
\][/tex]
- Next, multiply the area of the base by the height to get the volume:
[tex]\[
V = 201.06 \, \text{cm}^2 \times 6 \, \text{cm} \approx 1206.37 \, \text{cm}^3
\][/tex]
5. Round the result to the nearest two decimal places:
- The volume of the cylinder is approximately:
[tex]\[
1206.37 \, \text{cm}^3
\][/tex]
So, the volume of the cylinder with a diameter of 160 mm and height of 6 cm is approximately [tex]\(1206.37 \, \text{cm}^3\)[/tex], rounded to the nearest two decimal places.
