Number 5
4 marks · NormalA solid cuboid has length 10.2 cm, width 4.8 cm (both measured to the nearest 0.1 cm), and height 6.0 cm (measured to the nearest 0.5 cm).
Write down the lower and upper bounds for the height of the cuboid.
Calculate the lower and upper bounds for the volume of the cuboid. Give your answers correct to 3 significant figures.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) Lower bound: 5.75 cm, Upper bound: 6.25 cm
(b) Lower: 10.15 × 4.75 × 5.75 = 277 cm³; Upper: 10.25 × 4.85 × 6.25 = 310 cm³ (3 s.f.) cm³
Common mistakes: Confusing lower/upper bounds (using wrong direction for multiplication)
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Marking points
B1 (a) · 1 mark · Lower bound: 6.0 - 0.25 = 5.75 cm
B2 (a) · 1 mark · Upper bound: 6.0 + 0.25 = 6.25 cm
M1 (b) · 1 mark · Uses correct bounds for all dimensions; multiplies lower bounds for lower bound, upper bounds for upper bound.
A1 (b) · 1 mark · Rounds each volume answer to 3 s.f.
Worked solution
a) Height bounds: 6.0 cm ± 0.25 cm = 5.75 to 6.25 cm. b) Length: 10.2 ± 0.05, width: 4.8 ± 0.05. Lower volume: 10.15 × 4.75 × 5.75 = 276.7 (≈277 cm³); Upper: 10.25 × 4.85 × 6.25 = 310.1 (≈310 cm³), both to 3 s.f.