WAEC Mathematics 2012 Objective — Question 48

Question 48 of 50 from the West African Examinations Council (WAEC) Mathematics 2012 Objective paper, with the correct answer and a full explanation.

The volume of a cuboid is 54cm³. If the length, width and height are in the ratio 2:1:1 respectively, find its total surface area.

A. 108cm²
B. 90cm²Correct
C. 85cm²
D. 75cm²

Explanation

Let L:B:H = 2:1:1, so L=2H, B=H. Volume = L×B×H = 2H×H×H = 2H³ = 54, H³=27, H=3. So L=6, B=3, H=3. Total surface area = 2LB+2LH+2BH = 2(6×3)+2(6×3)+2(3×3) = 36+36+18 = 90cm².

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