Question

If the diameter of a sphere is decreased by 25%, then by what percent its curved area would decrease ?

(1) 43.75% (2) 50%
(3) 37% (4) none of these

Answer 1

D1 = 100x

D2 = 75x

R1 = 100x/2

R2 =75x/2

So..

Let the areas be A1 and A2 as initial and final respectively
$\frac{a2}{a1} = {( \frac{r2}{r1} )}^{2} \\ \\ or. \: \frac{a2}{a1} = {( \frac{ \frac{75x}{2} }{ \frac{100x}{2} } ) }^{2} = {0.75}^{2} \\ \\ or. \: (1 - \frac{a2}{a1} ) = 1 - 0.5625 = 0.4375 \\ \\ or. \: \: \frac{a1 - a2}{a1} \% = 43.75\%$

Hence (a) 43.75% is ur required answer.
Proud to help you.