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

Analyze the question: We have a cuboid with volume 54 cm³ and dimensions in the ratio 2:1:1 (length : width : height). We need the total surface area.

Concept:

• Volume = l × w × h
• Total surface area = 2(lw + lh + wh)

Solution:

Let the width = x, height = x, length = 2x.

Volume = 2x · x · x = 2x³ = 54 x³ = 27 x = 3

So length = 6 cm, width = 3 cm, height = 3 cm.

Check: 6 × 3 × 3 = 54 ✓

Total surface area = 2(lw + lh + wh) = 2(6×3 + 6×3 + 3×3) = 2(18 + 18 + 9) = 2(45) = 90 cm²

Answer: 90 cm², which is option B.

Tip: When given a ratio and a volume, introduce a single unknown (x) for the common multiplier, solve for it using the volume, then substitute back. Always check by recomputing the volume before moving on to the surface area.