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The base length, base width and height of a rectangular pyramid are decreased by 25%, 20% and 40% respectively. By how much percentage should the height of the pyramid be increased, so that the volume of the final pyramid becomes 17% more than that of the initial pyramid?

The base length, base width and height of a rectangular pyramid are decreased by 25%, 20% and 40% respectively. By how much percentage should the height of the pyramid be increased, so that the volume of the final pyramid becomes 17% more than that of the initial pyramid? Correct Answer 225%

Given:

Base length, base width and height of a rectangular pyramid are decreased by 25%, 20% and 40% respectively

Formula used:

Initial volume of rectangular pyramid = V = 1/3 × Base length × Base width × Height 

Calculation:

 Initial volume of rectangular pyramid = V = 1/3 × Base length × Base width × Height 

⇒ Decreased volume of pyramid = V' = 1/3 × × ×  

⇒ V' = 1/3 × (75% of Length) × (80% of width) × (60% of Height) 

⇒ V' = (0.75 × 0.8 × 0.6) × V = 0.36 V 

Now, 

Required volume of pyramid = (100 + 17)% of V = 1.17V 

∵ Volume of pyramid is directly proportional to height 

⇒ Increase in height of pyramid = Increase in volume of pyramid = 1.17V – 0.36V = 0.81V 

∴ Percentage increase in height = (0.81V/0.36V) × 100 = 225% 

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