A lean-to firewood store is built against a garden wall. Its triangular end has a right angle, with base 40 cm and height 25 cm, and the store runs 150 cm a...
Question 1 Report
A lean-to firewood store is built against a garden wall. Its triangular end has a right angle, with base 40 cm and height 25 cm, and the store runs 150 cm along the wall, as shown. Before winter sets in, the family wants to check how many loads of logs the store can hold.
- Work out the area of the triangular end. (2)
- Give the volume of the firewood store in litres. (2)
Answer Details
The firewood store is a triangular prism: a right-angled triangular cross-section that runs a fixed length along the wall. Its volume is \( V = \text{cross-sectional area} \times \text{length} \).
- The triangular end has a right angle, so its base and height are the two shorter sides: \[ \text{Area} = \frac{1}{2} \times 40 \times 25 = 500 \text{ cm}^2 \] [2] (1 for \(\frac{1}{2} \times 40 \times 25\), 1 for 500 cm\(^2\))
- Multiplying the cross-sectional area by the length the store runs along the wall:\[ V = 500 \times 150 = 75000 \text{ cm}^3 \]Since \(1\) litre \(= 1000\) cm\(^3\), this is \( 75000 \div 1000 = 75 \) litres. [2] (1 for \(500 \times 150\), 1 for converting to 75 litres)
Treating any solid with a constant cross-section (prism) as area times length is the general method that also applies to cylinders, and here it avoids having to find any missing hypotenuse.
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