The surface areas of two spheres are in the ratio 1:4, then the ratio

1.	The surface areas of two spheres are in the ratio 1:4, then the ratio of their volumes is ……A) 1 : 8 B) 1 : 64 C) 1 : 12 D) 1 : 16
Answer» Correct option is: A) 1 : 8 Given that \(\frac {S_1}{S_2} = \frac 14\) \(\Rightarrow\) \(\frac {4\pi r_1^2}{4\pi r_2^2} = \frac 14\) \(\Rightarrow\) \((\frac {r_1}{r_2})^2 = \frac 14 = (\frac 12)^2\) \(\Rightarrow\) \(\frac {r_1}{r_2}\) = \(\frac 12\) Now, \(\frac {V_1}{V_2} \) = \(\frac {\frac 43 \pi r^3_1}{\frac 43 \pi r^3_2} = (\frac {r_1}{r_2})^3 = (\frac 12)^3 = \frac 18\) Hence, the ratio of their volumes is 1 : 8 Correct option is: B) 1 : 8

The surface areas of two spheres are in the ratio 1:4, then the ratio of their volumes is ……A) 1 : 8 B) 1 : 64 C) 1 : 12 D) 1 : 16

Answer»

Correct option is: A) 1 : 8

Given that \(\frac {S_1}{S_2} = \frac 14\)

\(\Rightarrow\) \(\frac {4\pi r_1^2}{4\pi r_2^2} = \frac 14\)

\(\Rightarrow\) \((\frac {r_1}{r_2})^2 = \frac 14 = (\frac 12)^2\)

\(\Rightarrow\) \(\frac {r_1}{r_2}\) = \(\frac 12\)

Now, \(\frac {V_1}{V_2} \) = \(\frac {\frac 43 \pi r^3_1}{\frac 43 \pi r^3_2} = (\frac {r_1}{r_2})^3 = (\frac 12)^3 = \frac 18\)

Hence, the ratio of their volumes is 1 : 8

Correct option is: B) 1 : 8