Question
Download Solution PDFThe length, breadth and height of a cuboid are in the ratio 1 ∶ 2 ∶ 3. The length, breadth and height of the cuboid are increased by 200%, 300% and 300%, respectively. Then compared to the original volume, the increase in the volume of the cuboid will be :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3.
Formula used:
Volume of cuboid = Length(L) × Breadth(B) × Height(H)
Calculation:
Let the Length, breadth and height of the cuboid be 100, 200, and 300 respectively.
Volume of cuboid = 100 × 200 × 300 = 6000000
Length increased by 200%, Breadth increase by 300% and height by 300%
Now, new length = 300, breadth = 800 and height = 1200 respectively
⇒ new volume of cuboid = 300 × 800 × 1200
= 288000000
Increase in volume = (new volume of the cuboid – the volume of the cuboid)/volume of the cuboid
= (288000000 – 6000000)/6000000
= 282000000/6000000
= 47 times
∴ The increase in the volume of the cuboid will be 47 times.
Last updated on Jul 7, 2025
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