KVPY SA Exam 2013 Question Paper

Question : 64 of 80

Marks: +1, -0

Suppose the height of a pyramid with a square base is decreased by p% and the lengths of the sides of its square base are increased by p% (where p > 0). If the volume remains the same, then

50 < p < 55
55 < p < 60
60 < p < 65
65 < p < 70

Validate

Solution:

1/3(x^2)y=1/3x^2({100+p}/100)^2

({100-p}/100)

⇒ p^2 + 100p - 100^2 = 0

⇒p=√12500-50

60 < p < 65

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