Question

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

(a) 50 < p < 55

(b) 55 < p < 60

(c) 60 < p < 65

(d) 65 < p < 70

Answer 1

Answer is : (c) 60 < p < 65

Let the side of square base of pyramid is x m and height of pyramid is y m.

Volume of pyramid

= 1/3 area of base x height = 1/3 x²y

When x is increased by p%, then new length = x + p% of x = (100+p/100)x

When y is decreased by p%, then new height

= y - p% of y = (100-p/100)y

Now, volume is same.