Question

10. If the ratio of the volumes of two spheres is 1:8, then the ratio of their surface area is
(C) 1:8
0
(d) 1:16
(b) 1:4
(a) 1:2
()
0​

Answer 1

$\huge \boxed{ \colorbox{aqua}{Answer : - }}$

$Volume \: of \: a \: sphere \: of \: radius \: 'r' = \frac{4}{3}\pi {r}^{3}$

• Let r¹ be the radius of the first sphere and r² be the radius of the second sphere .

Given ratio of their volume is : V¹ : V²=1:8.

$\frac{4}{3} \pi {r}^{3}1 : \frac{4}{3}\pi \: r3 { }^{2} = 1: 8$

${r1}^{2} : {r2}^{3}$

$\implies \: r1 : r2 = 1 : 2$

$Surface \: area \: of \: sphere \: of \: radius \: 'r'=4\pi \: {r}^{2}$

• Now ratio of their surface area is S1 and S2.

$s1 : s2$

$= 4\pi \: r1 {}^{2} : 4\pi \: r2 {}^{2} h$

$\implies \: r1 {}^{2} \ratio \: r2 {}^{2}$

$= {1}^{2} \ratio \: 2 {}^{2}$

$\implies \: 1 \ratio \: 4$