The length (l) of a cuboidal cold storage is twice its breadth (b), while its…
2026
The length (l) of a cuboidal cold storage is twice its breadth (b), while its height (h) is half its breadth. If its volume is 1728 m3, what are its dimensions, in metres, in l × b × h order?
Answer: D. 24 × 12 × 6 — ConceptThe volume of a cuboid equals the product of its length, breadth, and height: V = l × b × h. When all three dimensions are expressed through one…
- A.
12 × 6 × 18
- B.
12 × 9 × 17
- C.
12 × 10 × 9
- D.
24 × 12 × 6
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Show answer & explanation
Correct answer: D
Concept
The volume of a cuboid equals the product of its length, breadth, and height: V = l × b × h.
When all three dimensions are expressed through one variable, substitute those relations into the volume formula and solve for that variable.
Application
Let the breadth be b metres. Then l = 2b and h = b/2.
Substitute into the volume formula: 1728 = (2b) × b × (b/2).
Simplifying gives b3 = 1728, so b = 12 metres.
Therefore, l = 2 × 12 = 24 metres and h = 12/2 = 6 metres.
Cross-check
The product 24 × 12 × 6 is 1728, and the relations 24 = 2 × 12 and 6 = 12/2 both hold.
Hence, the dimensions in l × b × h order are 24 × 12 × 6 metres.