Jackson is trying to find the density, in g/cm³, of a block of wood - Edexcel - GCSE Maths - Question 1 - 2018 - Paper 2

Using the upper and lower bounds:

• Lower bound volume: $V_{min} = 13.15 imes 15.95 imes 21.65$ $V_{min} = 4301.867875$ cm³

• Upper bound volume: $V_{max} = 13.25 imes 16.05 imes 21.75$ $V_{max} = 4536.405875$ cm³

The measured mass is 1970 g, correct to the nearest 5 g:

• Lower bound: 1967.5 g
• Upper bound: 1972.5 g

Using the mass and the volume bounds to find density:

• Lower bound density: $\rho_{min} = \frac{1967.5}{4536.405875} \\ \rho_{min} \approx 0.4335 g/cm³$

• Upper bound density: $\rho_{max} = \frac{1972.5}{4301.867875} \\ \rho_{max} \approx 0.4597 g/cm³$

The density of the wood, given the bounds calculated, is:

• Between 0.4335 g/cm³ and 0.4597 g/cm³.

Rounding to 3 significant figures, the appropriate answer is:

• Density: 0.446 g/cm³.

This shows the density is constrained by the measurements taken and accounts for the precision indicated in the problem.