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

___ kg

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 (V) of the cylinder** using the formula:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius
- \( h \) is the height
- \( \pi \) is approximately 3.14

Given:
- \( r = 10 \) cm
- \( h = 8 \) cm

First, convert the dimensions to meters since the density is in kg/m³:
\[
r = 10 \text{ cm} = 0.1 \text{ m}
\]
\[
h = 8 \text{ cm} = 0.08 \text{ m}
\]

Now, substitute these values into the volume formula:
\[
V = 3.14 \times (0.1)^2 \times 0.08
\]
\[
V = 3.14 \times 0.01 \times 0.08
\]
\[
V = 3.14 \times 0.0008
\]
\[
V = 0.002512 \text{ m}^3
\]

2. **Calculate the mass (m)** of the cylinder using the formula:
\[
m = \text{density} \times V
\]
Given that the density is \( 8000 \) kg/m³:
\[
m = 8000 \times 0.002512
\]
\[
m = 20.096 \text{ kg}
\]

3. **Round the mass to the nearest tenth**:
The mass of the cylinder is approximately:
\[
m \approx 20.1 \text{ kg}
\]

Thus, the mass of the steel cylinder is \( \boxed{20.1} \) kg.