The organisers arrange energy drink crates into a perfect cube stack for the sports day refreshment stall, using 125 crates in total. Write down the whole n...
Question 1 Report
The organisers arrange energy drink crates into a perfect cube stack for the sports day refreshment stall, using 125 crates in total.
- Write down the whole number that, when cubed, gives 125. (1)
- Work out the value of that number squared. (1)
- A second stack uses one fewer crate along each edge of the cube. Work out how many crates the second stack contains. (2)
Answer Details
A cube number is a whole number multiplied by itself three times; finding a cube root means finding the whole number that produces a given cube.
(a) Testing whole numbers, \(5 \times 5 \times 5 = 125\), so the cube root of 125 is 5. [1 mark]
(b) Squaring this value: \(5^2 = 25\). [1 mark]
(c) Using one fewer crate along each edge gives a cube of side \(5 - 1 = 4\), so the second stack contains \(4^3 = 4 \times 4 \times 4 = 64\) crates. [2 marks]
Reducing the edge length by just 1 crate does not reduce the total by a small fixed amount: because volume scales with the cube of the edge length, the total drops from 125 crates to 64, a loss of 61 crates from removing only one layer off each edge.
Download The App On Google Playstore
Everything you need to excel in your exams
