Question

If the ratio of volumes of two spheres is 1:8 find ratio of their surface area

Answer 1

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

Volume of first : Volume of second = 1 : 8

$\frac{ \frac{4}{3} \pi \: {r1}^{3} }{ \frac{4}{3} \pi \: {r2}^{3} } = \frac{1}{8}$



$\frac{ {r1}^{3} }{ {r2}^{3} } = \frac{1}{8}$

$\frac{r1}{r2} = \sqrt[ 3 ]{ \frac{1}{8} }$

$\frac{r1}{r2 } = \frac{1}{2}$

Now,


Surface area of 1st : Surface area of 2nd

$\frac{4\pi \: {(r1)}^{2} }{4\pi \: {(r2)}^{2} } \\ \\ \frac{ {(r1)}^{2} }{ {(r2) }^{2} }$

$\frac{1}{4}$

ratio of surface area is 1 : 4

Answer 2

Answer:

1:4

Step-by-step explanation:

vol.of 1st:vol.of 2nd = 1:8