iGCSE Mathematics (0580) : C5.4 Carry out calculations involving the surface area and volume iGCSE Style Questions Paper 1

Question

The diagram shows a prism. The cross-section of the prism is an equilateral triangle.

Draw a net of the prism on the \(1cm^{2}\) grid.

▶️ Answer/Explanation

Answer: Correct net

Solution:

An equilateral triangle prism net consists of:
- Three identical rectangles (side faces)
- Two equilateral triangles (top and bottom bases)
All sides must be equal in length since it’s equilateral
The rectangles should be adjacent to the sides of the triangles
The net should fold into a 3D prism without gaps or overlaps

The exact dimensions depend on the given prism size, but the shape arrangement remains consistent as described.

Question

The diagram shows one face of a cuboid on a 1 cm² grid.

The cuboid has a volume of 24 cm³.
Complete a net of this cuboid.

▶️ Answer/Explanation

Solution

Ans: The cuboid has dimensions 4 cm × 3 cm × 2 cm.

1. From the grid, we observe one face measures 4 cm × 3 cm.

2. Let the unknown dimension be x cm.

3. Volume = 4 × 3 × x = 24 cm³.

4. Solving: 12x = 24 → x = 2 cm.

5. Thus, the cuboid’s net includes six faces: two 4×3, two 4×2, and two 3×2 rectangles.

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