Question

The densities of three metal alloys, A, B and C, are in the ratio

13:15:21
1m³ of alloy B has a mass of 8600 kg.
Work out the difference between the mass of 5m^3 of alloy A and 3m³ of alloy C. Give your answer correct to 3 significant figure

Answer 1

The difference between the mass of 5m³ of Alloy A and 3m³ of Alloy C is about 1146.67 kg, correct to three significant figures.

How to find difference between masses?

To solve this problem, determine the densities of the three metal alloys (A, B, and C) based on their given ratio:

Given that 1m³ of alloy B has a mass of 8600 kg, the density of B (
`\( \rho_B \)`) is calculated as:

`\[ \rho_B = \frac{\text{Mass of B}}{\text{Volume of B}} = \frac{8600 \, \text{kg}}{1 \, \text{m}^3} = 8600 \, \text{kg/m}^3 \]`

The ratio of densities is given as 13:15:21 for A:B:C.

For Alloy A (
`\( \rho_A \)`):

`\[ \rho_A = (13)/(15) * \rho_B = (13)/(15) * 8600 \, \text{kg/m}^3 = 7453.33 \, \text{kg/m}^3 \]`

For Alloy C (
`\( \rho_C \)`):

`\[ \rho_C = (21)/(15) * \rho_B = (21)/(15) * 8600 \, \text{kg/m}^3 = 12040 \, \text{kg/m}^3 \]`

Mass of 5m³ of Alloy A:

Mass of 5m³ of A = Volume of A ×
`\rho_A`

= 5 m³ × 7453.33 kg/m³

= 37266.67 kg

Mass of 3m³ of Alloy C:

Mass of 3m³ of C = Volume of C ×
`\rho_C`

= 3 m³ × 12040 kg/m³

= 36120 kg

Calculate the difference in mass:

Difference = Mass of 5m³ of A - Mass of 3m³ of C

= 37266.67 kg - 36120 kg

= 1146.67 kg

So, the difference between the mass of 5m³ of Alloy A and 3m³ of Alloy C is approximately 1146.67 kg, correct to three significant figures.