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

1 answer

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.