Question

A steel cylinder has a base with a radius of 10 cm and height of 8 cm. If the density of the cylinder is 8,000 kg/m3 , find the mass of the cylinder in kilograms. Use π=3.14 and round your answer to the nearest tenth.

Answer 1

To find the mass of the steel cylinder, we first need to calculate its volume and then use the density to find the mass.

1. **Calculate the volume of the cylinder** using the formula:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

Given:
- \( r = 10 \) cm = \( 0.1 \) m (since 1 m = 100 cm),
- \( h = 8 \) cm = \( 0.08 \) m.

Now substituting these values into the volume formula:
\[
V = 3.14 \times (0.1)^2 \times 0.08
\]

First, calculate \( (0.1)^2 \):
\[
(0.1)^2 = 0.01 \, \text{m}^2
\]

Now calculate the volume:
\[
V = 3.14 \times 0.01 \times 0.08 = 3.14 \times 0.0008 = 0.002512 \, \text{m}^3
\]

2. **Calculate the mass of the cylinder** using the formula:
\[
\text{mass} = \text{density} \times \text{volume}
\]

Given that the density is \( 8000 \, \text{kg/m}^3 \):
\[
\text{mass} = 8000 \, \text{kg/m}^3 \times 0.002512 \, \text{m}^3
\]

Calculate the mass:
\[
\text{mass} = 8000 \times 0.002512 = 20.096 \, \text{kg}
\]

3. **Round the mass to the nearest tenth**:
\[
\text{mass} \approx 20.1 \, \text{kg}
\]

Thus, the mass of the cylinder is **20.1 kg**.