Question

please tell me whose rank is genius and ace please answer this



69. The ratio of the volumes of

two

spheres is 8:27. The ratio

between

their surface areas is

O 1)2:3

2) 4:27

)

O 3) 8:9

O 4)4:9​

Answer 1

Answer:

4) 4:9

Step-by-step explanation:

Volume of Sphere:

$V=\frac{4}{3}\pi r^3$

So,

$\dfrac{V_1}{V_2}= \dfrac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3} = \dfrac{r_1^3}{r_1^3}=\dfrac{8}{27} \\\\\rightarrow \dfrac{r_1}{r_2}=\dfrac{2}{3}$

Now, Surface Area of a Sphere:

$S=4\pi r^2$

So,

$\dfrac{S_1}{S_2}=\dfrac{4\pi r_1^2}{4\pi r_2^2} = \left(\dfrac{r_1}{r_2}\right)^2 = \left(\dfrac{2}{3}\right)^2 = \dfrac{4}{9}$