Question

If the diameter of a sphere is decreased by 20%, by what percent will it's surface area decrease? (with steps)

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%

Answer 2

Decraes = 4/3ΠR³ ÷ 4/3Πr³
= R³/ r³
= x³/ (x-20)³

There fore 80% is decrease