Let's find the volume of a cylinder using the given dimensions.
Step 1: Convert units
First, we need to ensure that all measurements are in the same unit. The height is already given in centimeters. However, the diameter is provided in millimeters. Let's convert the diameter from millimeters to centimeters:
[tex]\[ \text{Diameter} = 30 \text{ mm} = \frac{30}{10} = 3 \text{ cm} \][/tex]
Step 2: Calculate the radius
The radius [tex]\(r\)[/tex] is half of the diameter:
[tex]\[ r = \frac{\text{Diameter}}{2} = \frac{3 \text{ cm}}{2} = 1.5 \text{ cm} \][/tex]
Step 3: Use the volume formula for a cylinder
The formula for the volume [tex]\(V\)[/tex] of a cylinder is:
[tex]\[ V = \pi r^2 h \][/tex]
where [tex]\(h\)[/tex] is the height and [tex]\(r\)[/tex] is the radius. Plugging in the values we have:
[tex]\[ r = 1.5 \text{ cm} \][/tex]
[tex]\[ h = 9.5 \text{ cm} \][/tex]
Step 4: Calculate the volume
[tex]\[ V = \pi (1.5 \text{ cm})^2 (9.5 \text{ cm}) \][/tex]
[tex]\[ V = \pi (2.25 \text{ cm}^2) (9.5 \text{ cm}) \][/tex]
[tex]\[ V = \pi (21.375 \text{ cm}^3) \][/tex]
Step 5: Approximate the volume using [tex]\(\pi\)[/tex]
Using the value of [tex]\(\pi \approx 3.14159265359\)[/tex], we can calculate the final volume:
[tex]\[ V \approx 3.14159265359 \times 21.375 \text{ cm}^3 \][/tex]
[tex]\[ V \approx 67.15154297048183 \text{ cm}^3 \][/tex]
So, the volume of the cylinder is approximately [tex]\(67.1515 \text{ cm}^3\)[/tex].
