The length, breadth, and height of a cuboid are in the ratio 4 : 9 : 12. The…
2026
The length, breadth, and height of a cuboid are in the ratio 4 : 9 : 12. The length, breadth, and height are increased by 50%, 100%, and 100%, respectively. The increase in the volume of the cuboid is:
Answer: B. 5 times — ConceptFor a cuboid, volume is the product of its three dimensions: V = l × b × h. When the dimensions change independently, the new-to-old volume ratio…
- A.
2 times
- B.
5 times
- C.
8 times
- D.
6 times
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Show answer & explanation
Correct answer: B
Concept
For a cuboid, volume is the product of its three dimensions: V = l × b × h.
When the dimensions change independently, the new-to-old volume ratio equals the product of their scale factors. An increase of p% gives a scale factor of 1 + p/100.
Application
Let the original volume be V.
The length scale factor is 1 + 50/100 = 3/2.
The breadth scale factor is 1 + 100/100 = 2.
The height scale factor is 1 + 100/100 = 2.
Therefore, the new volume is V × 3/2 × 2 × 2 = 6V.
The increase is 6V − V = 5V, which is 5 times the original volume.
Cross-check
Take the original dimensions as 4x, 9x, and 12x. After the increases, they become 6x, 18x, and 24x.
The volume ratio is (6 × 18 × 24)/(4 × 9 × 12) = 6, so the added volume is 6V − V = 5V. Hence, the increase is 5 times the original volume.