A car workshop orders a cuboid storage cabinet to hold spare parts, with a volume of 2.4 m\(^3\). The cabinet is 2 m high and 1.2 m wide. The foreman needs ...
Question 1 Report
A car workshop orders a cuboid storage cabinet to hold spare parts, with a volume of 2.4 m\(^3\). The cabinet is 2 m high and 1.2 m wide. The foreman needs the missing dimension before the cabinet is delivered and installed.
- Work out the length of the cabinet. (4)
Answer Details
The cuboid volume formula links all three dimensions, so when the volume and two dimensions are already known, the formula is rearranged to find the missing length.
Substituting the known values into \(V = l \times w \times h\):
\[2.4 = l \times 1.2 \times 2 \quad \textbf{[1 mark]}\]
\[2.4 = 2.4l \quad \textbf{[1 mark]}\]
Dividing both sides by 2.4:
\[l = \frac{2.4}{2.4} \quad \textbf{[1 mark]}\]
\[l = 1 \text{ m} \quad \textbf{[1 mark]}\]
Exam tip: when two of a cuboid's three dimensions are known along with its volume, multiply the two known dimensions together first, then divide the volume by that product to find the missing one.
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