Question

volume of two spheres are in the ratio of 67:27. the ratio of their surface area is​

Answer 1

Question:

The volume of two spheres are in the ratio of 64:27.

the ratio of their surface area is

Solution:

Let,

the radius of two spheres A and B be

m and n respectively.

As we know,

volume of sphere = 4/3×π×(radius)^3

so,

$\mathrm{ \frac{volume \: of \: sphere \: A}{volume \: of \: sphere \: B} = \frac{ \frac{4}{3}\pi {m}^{3} }{ \frac{4}{3}\pi {n}^{3} } } = \frac{64}{27}$

$\mathrm{ \frac{ \cancel{ \frac{4}{3} \pi} {m}^{3} }{ \cancel{ \frac{4}{3}\pi } {n}^{3} } = \frac{64}{27} } \\ \\ \mathrm{ {( \frac{m}{n}) }^{3} } = { (\frac{4}{3}) }^{3} \\ \\ \boxed{ \bf{ \frac{m}{n} = \frac{4}{3} }}$

Now,

as we know

surface area of sphere= 4×π×(radius)^2

so,

ratio of the surface area of two spheres

= (4πm^2) / (4πn^2)

= m^2 / n^2

= ( 4 /3) ^2

= 16 / 9

Therefore,

the ratio of the surface of the spheres A and B is 16 : 9 .

Answer 2

Answer:

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