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
8
,
000

kg
/
m
3
, find the mass of the cylinder in kilograms. Use π=3.14
𝜋
=
3.14
and round your answer to the nearest tenth.

Answer 1

To find the mass of the steel cylinder, we can use the following steps:

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.

2. **Convert the radius and height from centimeters to meters**:
- Radius \( r = 10 \) cm = \( 0.10 \) m,
- Height \( h = 8 \) cm = \( 0.08 \) m.

3. **Substitute the values into the volume formula**:
\[
V = \pi (0.10)^2 (0.08)
\]
\[
= 3.14 \times 0.01 \times 0.08
\]
\[
= 3.14 \times 0.0008
\]
\[
= 0.002512 \text{ m}^3
\]

4. **Calculate the mass** using the formula:
\[
\text{mass} = \text{density} \times \text{volume}
\]
Given that the density of the steel cylinder is \( 8,000 \) kg/m³:
\[
\text{mass} = 8,000 \text{ kg/m}^3 \times 0.002512 \text{ m}^3
\]
\[
= 20.096 \text{ kg}
\]

5. **Round the answer to the nearest tenth**:
- The mass of the cylinder is approximately \( 20.1 \) kg.

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