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.(1 point)
kg

Answer 1

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

1. **Calculate the Volume of the Cylinder**:
The formula for the volume \( V \) of a cylinder is given by:

\[
V = \pi r^2 h
\]

Where:
- \( r \) is the radius
- \( h \) is the height
- \( \pi \) is approximately \( 3.14 \)

Given:
- Radius \( r = 10 \) cm = \( 0.1 \) m (since we need to convert cm to m)
- Height \( h = 8 \) cm = \( 0.08 \) m

Plugging in the values:

\[
V = 3.14 \times (0.1)^2 \times 0.08
\]

\[
V = 3.14 \times 0.01 \times 0.08
\]

\[
V = 3.14 \times 0.0008
\]

\[
V = 0.002512 \, \text{m}^3
\]

2. **Calculate the Mass of the Cylinder**:
The mass \( m \) can be calculated using the volume and density. The formula is:

\[
m = \text{density} \times V
\]

Given the density of the cylinder is \( 8000 \, \text{kg/m}^3 \):

\[
m = 8000 \, \text{kg/m}^3 \times 0.002512 \, \text{m}^3
\]

\[
m = 20.096 \, \text{kg}
\]

3. **Round to the Nearest Tenth**:
Rounding \( 20.096 \) kg to the nearest tenth gives us:

\[
m \approx 20.1 \, \text{kg}
\]

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