iGCSE Mathematics (0580) :C5.4 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder. iGCSE Style Questions Paper 3

Question

(a) A closed box, in the shape of a cuboid, has length 5cm, width 4cm and height 2cm.

(i) Draw a net of the box on the 1cm² grid.

(ii) A container is a cube with volume 1m³. Work out the maximum number of these boxes that can be packed into this container.

(b) A shop sells three different sized boxes of rice. The boxes all have the same cost per kilogram.

(i) Work out the cost in rupees of box B.

(ii) $1 = 64 rupees. Calculate the mass of box C. Give your answer in kilograms.

▶️ Answer/Explanation

(a)(i): A correct ruled net showing all faces of the cuboid (5cm×4cm, 5cm×2cm, 4cm×2cm) arranged flat.

(a)(ii): 25,000 boxes (Convert 1m³ to cm³ = 1,000,000cm³; Box volume = 5×4×2 = 40cm³; 1,000,000÷40 = 25,000).

(b)(i): ₹144 (Box A: ₹96/2kg = ₹48/kg; Box B: 3kg × ₹48 = ₹144).

(b)(ii): 2.1kg ($3.50 × 64 = ₹224; ₹224 ÷ ₹48/kg = 4.666…kg; Subtract Box A’s 2kg = 2.666…kg ≈ 2.1kg).

(c): 7.5×10⁻² litres (75cm³ = 0.075 litres = 7.5×10⁻² in standard form).

Question

The diagram shows the net of a triangular prism on a $1cm^{2}$ grid.

(a) Write down the mathematical name for the type of triangle shown on the grid.

(b) (i) Measure the perpendicular height of the triangle.

(ii) Calculate the area of the triangle.

(iii) Calculate the volume of the triangular prism.

▶️ Answer/Explanation

Answers:

(a) Equilateral

(b)(i) 4.1 to 4.5 cm

(ii) 10.25 to 11.25 cm²

(iii) 61.5 to 67.5 cm³

Detailed Solution:

(a) All three sides measure 5cm on the grid → Equilateral triangle.

(b)(i) Use ruler vertically from base (5cm) to apex → ~4.3cm height.

(b)(ii) Area = ½ × base × height = 0.5 × 5 × 4.3 ≈ 10.75cm².

(b)(iii) Prism length = 6cm (from net diagram). Volume = Area × Length = 10.75 × 6 ≈ 64.5cm³.

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