Question

The diameter of a sphere I'd decreased by 20%. By what percent does its curved surface area decreased

Answer 1

Let the diameter of sphere be "d" curved surface area of sphere = 4πr2 = π (2r)2 = π(d)2 Given diameter of sphere decreases by 20% New diameter = d - (d/5) = 4d/5 New curved surface area = π(4d/5)2                     = (16/25) πd2 Change in surface area of sphere = πd2 – (16/25) πd2 = (9/25) πd2 decrease in curved surface area = [9/25) πd2/ πd2] x 100 = 36% Therefore surface area decreases by 36%