Question

a block of metal has a mass of (68.7\text{ kg}).
each (\text{cm}^3) of the metal has a mass of (8.1\text{ g}).
the block of metal is melted and then made into cylinders like the one below.

how many complete cylinders can be made?

a cylinder with length (7.4\text{ cm}) and radius (2.6\text{ cm})

not drawn accurately

Explanation:

⚡ Using what you learned: Density, Mass, and Volume · Unit Conversions

Step 1: Convert mass units

Convert the total mass of the metal block from kilograms to grams so that it matches the unit of density (\(\text{g/cm}^3\)).

$$ 68.7\text{ kg} \times 1000\text{ g/kg} = 68700\text{ g} $$

Step 2: Calculate total volume of metal

Calculate the total volume of the metal block using its mass and density (\(8.1\text{ g/cm}^3\)).

$$ \text{Total Volume} = \frac{68700\text{ g}}{8.1\text{ g/cm}^3} \approx 8481.4815\text{ cm}^3 $$

Step 3: Calculate volume of one cylinder

The cylinder has a radius \(r = 2.6\text{ cm}\) and a length/height \(h = 7.4\text{ cm}\).

$$ \text{Volume of one cylinder} = \pi r^2 h = \pi \times (2.6\text{ cm})^2 \times 7.4\text{ cm} $$

$$ \text{Volume of one cylinder} = \pi \times 6.76 \times 7.4 \approx 157.1156\text{ cm}^3 $$

Step 4: Calculate number of complete cylinders

Divide the total volume of metal by the volume of one cylinder and round down to the nearest whole number.

$$ \text{Number of cylinders} = \frac{8481.4815}{157.1156} \approx 53.98 $$

Rounding down gives 53 complete cylinders.

Answer:

53