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.

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 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.

   Given:

   • \( r = 10 \) cm = \( 0.1 \) m (since 1 m = 100 cm),
   • \( h = 8 \) cm = \( 0.08 \) m.

   Now substituting these values into the volume formula: \[ V = 3.14 \times (0.1)^2 \times 0.08 \]

   First, calculate \( (0.1)^2 \): \[ (0.1)^2 = 0.01 , \text{m}^2 \]

   Now calculate the volume: \[ V = 3.14 \times 0.01 \times 0.08 = 3.14 \times 0.0008 = 0.002512 , \text{m}^3 \]

2. Calculate the mass of the cylinder using the formula: \[ \text{mass} = \text{density} \times \text{volume} \]

   Given that the density is \( 8000 , \text{kg/m}^3 \): \[ \text{mass} = 8000 , \text{kg/m}^3 \times 0.002512 , \text{m}^3 \]

   Calculate the mass: \[ \text{mass} = 8000 \times 0.002512 = 20.096 , \text{kg} \]

3. Round the mass to the nearest tenth: \[ \text{mass} \approx 20.1 , \text{kg} \]

Thus, the mass of the cylinder is 20.1 kg.