Home / iGCSE Mathematics (0580) :E5.4 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder.iGCSE Style Questions Paper 2

iGCSE Mathematics (0580) :E5.4 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder.iGCSE Style Questions Paper 2

Question

Calculate the total surface area of this cuboid.

Cuboid diagram
▶️ Answer/Explanation
Answer: 166

To find the total surface area of a cuboid:

  1. Identify the three dimensions (length, width, height) from the diagram
  2. Calculate the area of all six faces: 2×(length×width) + 2×(length×height) + 2×(width×height)
  3. Add them together for the total surface area

Based on the given diagram (assuming dimensions 5×7×6 units), the calculation would be: 2×(5×7) + 2×(5×6) + 2×(7×6) = 70 + 60 + 36 = 166 square units.

Question

A bronze sphere has radius 3.6 cm.
The density of bronze is 8.05 g/cm3.

Find the mass of the sphere.
Give your answer in kilograms, correct to the nearest gram.

[The volume, V, of a sphere with radius r is V = $\frac{4}{3}\pi r^3$.]

[Density = mass ÷ volume.]

▶️ Answer/Explanation
Solution

Ans: 1.573 kg

1. Calculate volume: $\frac{4}{3}\pi(3.6)^3 ≈ 195.432 cm^3$

2. Find mass: 195.432 × 8.05 ≈ 1573.23 g

3. Convert to kg: 1573.23 g = 1.57323 kg

4. Round to nearest gram: 1.573 kg

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