A large wooden box, open at the top, needs to be lined with fabric on its inner floor and inner four side walls. The inner dimensions of the box are 2.5 m length, 1.8 m wide, and 1.2 m high. If the fabric comes in square pieces of side 50 cm, and 15% extra fabric is needed for cuts and overlaps, how many approximate fabric pieces should be purchased?

Correct — C. The box is open at the top, so line the floor and four walls only.

Floor = 2.5 × 1.8 = 4.5 m²
Four walls = 2(l + b) × h = 2(2.5 + 1.8) × 1.2 = 10.32 m²
Area to line = 4.5 + 10.32 = 14.82 m²

Add 15% = 14.82 × 1.15 = 17.043 m²
One piece = 0.5 m × 0.5 m = 0.25 m²
Pieces = 17.043 ÷ 0.25 = 68.17, rounded up to 69 → option (c)

Why the others are wrong

• (a)
  59 — 59 is 14.82 ÷ 0.25 = 59.28 with the fraction cut off. It skips the 15% allowance for cuts and overlaps.
• (b)
  62 — 62 pieces cover 62 × 0.25 = 15.5 m². That beats the bare 14.82 m² but falls short of the 17.04 m² the 15% allowance demands.
• (d)
  72 — 72 pieces cover 18 m², about 1 m² more than the 17.04 m² needed. 69 pieces already cover it, so 72 over-buys.

Lining a box is a surface area problem, and the first decision is which faces count. A closed box has six faces, 2(lb + bh + lh).

An open-top box loses the lid, leaving lb + 2(l + b)h. The four walls together are the floor's perimeter times the height.

Then add the wastage percentage to the area, divide by one piece's area in the same units, and round up, because a part-piece cannot be bought.

Key facts

• Four walls of a box = 2(l + b) × h.
• Open-top box area = lb + 2(l + b)h.
• 50 cm = 0.5 m, so a 50 cm square covers 0.25 m².
• A piece count rounds up: 68.17 pieces means 69 must be bought.

Common traps

• Using the closed-box formula 2(lb + bh + lh): it adds the 4.5 m² lid and gives about 89 pieces.
• Dividing by the side, 0.5, instead of the piece's area, 0.25: 17.043 ÷ 0.5 ≈ 34 pieces.

No directly related past PYQ was found.