Question

6. Ratio of volumes of two spheres is
8:27 then ratio of their curved surface
areas is ..... AP Mar. 2016 [ ]
A) 2:3
B) 4:27
C) 8:9
D) 4:9​

Answer 1

Answer:

D) 4:9​

Step-by-step explanation:

Let, their radius of two spheres are r1 and r2.

Then, $\frac{4}{3}\pi(r_1)^3 :\frac{4}{3}\pi(r_2)^3 = 8 : 27$

► $(r_1)^3 :(r_2)^3 = 8 : 27$

► $r_1 :r_2= 2 : 3$

After that, the ratio of their curved surface

= 4π(r1)² : 4π(r2)²

= (r1)² : (r2)²

= 2² : 3²

= 4 : 9

Answer 2

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \pink{Solution\::}$

$➩ \frac{volume \: of \: 1st \: sphere}{volume \: of \: 2nd \: sphere} = \frac{8}{27}$

$➩ \frac{\frac{4}{3} \pi {r}^{3}}{\frac{4}{3} \pi {R}^{3}} = \frac{8}{22}$

$➩ \frac{ {r}^{3} }{ {R}^{3} } = \frac{8}{27}$

$➩ \frac{r}{R} = \frac{2}{3}$

$\green{According \: to \: the \: question\::}$

$➩ \frac{surface \: area \: of \: 1st \: sphere}{surface \: area \: of \: 2nd \: sphere} = \frac{4\pi {r}^{2} }{4\pi {R}^{2} }$

$➩\frac{surface \: area \: of \: 1st \: sphere}{surface \: area \: of \: 2nd \: sphere} = \frac{ {2}^{2} }{ {3}^{2} }$

$➩\frac{surface \: area \: of \: 1st \: sphere}{surface \: area \: of \: 2nd \: sphere} = \frac{4}{9}$

$\: \: \: \: \: \: \red{Hence, D \: is \: the \: Answer.\:}$