A depot keeps a reference table showing the volume of cube-shaped fuel tanks for different side lengths, so that staff can order the correct size without re...
Question 1 Report
A depot keeps a reference table showing the volume of cube-shaped fuel tanks for different side lengths, so that staff can order the correct size without recalculating each time. Some values in the table are missing.
| Side length (m) | 2 | 3 | ? | 6 |
|---|---|---|---|---|
| Volume (m³) | 8 | 27 | 125 | ? |
- Work out the missing side length, given that its cube is \(125\). (2)
- Work out the missing volume for a side length of \(6\) m. (2)
Answer Details
The table links a cube's side length to its volume by cubing; both parts use this relationship in opposite directions.
- (a) [2]. If the side length cubed is \(125\), the side length is \(\sqrt[3]{125} = 5\) m, since \(5\times5\times5 = 125\). One mark for identifying the cube root as the correct operation, one for the value \(5\) m.
- (b) [2]. For a side length of \(6\) m, the volume is \(6^3 = 6\times6\times6 = 216\ \text{m}^3\). One mark for using the correct formula (side length cubed), one for the value \(216\ \text{m}^3\).
Cubing a side length gives volume; taking a cube root of a volume reverses this to give the side length. Keep clear which direction the table is being read in each part.
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