The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid.
A. 77%
B. 75%
C. 88%
D. 98%
E. 99%
Answer: Option D
Solution(By Examveda Team)
Let each side of the cuboid be 10 unit initially. Initial Volume of the cuboid, = length * breadth * height = 10 × 10 × 10 = 1000 cubic unit. After increment dimensions become, Length = (10 + 10% of 10) = 11 unit. Breadth = (10 + 20% of 10) = 12 unit. Height = (10 + 50% of 10) = 15 unit. Now, present volume = 11 × 12 × 15 = 1980 cubic unit. Increase in volume = 1980 - 1000 = 980 cubic unit. % increase in volume = $$\frac{{980}}{{1000}} \times 100 = 98\% $$ Mind Calculation Method: 100 == 50%↑(height effects) ==> 150 == 20%↑(breadth) ==> 180 == 10%↑(length effects) ==> 198 Change in volume = 98%[We can take net percentage change in any order]
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How a cuboid's length breadth and height can be same.
It will become cube.