To find the mass of the steel cylinder, we first need to calculate its volume using the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
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 use meters for the density),
- Height \( h = 8 \) cm = 0.08 m.
Now, we can plug in the values:
\[ V = 3.14 \times (0.1)^2 \times 0.08 \]
Calculating \( (0.1)^2 \):
\[ (0.1)^2 = 0.01 \]
Now substituting back into the volume formula:
\[ V = 3.14 \times 0.01 \times 0.08 \] \[ V = 3.14 \times 0.0008 \] \[ V = 0.002512 , \text{m}^3 \]
Now that we have the volume, we can find the mass using the formula:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
Given the density is 8000 kg/m³, we can calculate:
\[ \text{Mass} = 8000 , \text{kg/m}^3 \times 0.002512 , \text{m}^3 \] \[ \text{Mass} = 20.096 , \text{kg} \]
Rounding to the nearest tenth, the mass of the cylinder is:
\[ \text{Mass} \approx 20.1 , \text{kg} \]
Therefore, the mass of the cylinder is 20.1 kg.