Question

The volume of two sphere are in the ratio 64:17.find the ratio of their surface area​

Answer 1

Radius of big sphere = R
Radius of small sphere = r.
Volume of bigger sphere
Volume of smaller sphere
Given,
Volume of bigger sphere : Volume of smaller sphere = 64 : 27.


Surface area of bigger sphere
Surface area of smaller sphere
Hence, Surface area of bigger sphere: Surface area of smaller sphere =
Thus, the ratio of their surface areas = 16 : 9

Answer 2

Given :-

▪ The volume of two sphere are in the ratio 64 : 17

To Find :-

▪ the ratio of their surface area

Solution :-

Given that the ratio of volume of two spheres is 64 : 17. So, Let us find the ratio of their radii.

We know,

⇒ Volume of Sphere = 4/3 πr³

Let the radius of bigger sphere be R and that of the smaller one be r.

⇒ (4/3 πR³) / (4/3 πr³) = 64 / 17

⇒ R³ / r³ = 64 / 17

⇒ R / r = 4 / (17)⅓ ...(1)

Now, We have to find the ratio of their surface area.

We have,

⇒ Surface area of Sphere = 4πr²

So, Ratio can be found as:

⇒ 4πR² / 4πr²

⇒ R² / r²

⇒ { 4 / (17)⅓ }²

⇒ 16 / (17)⅔

Hence, The ratio of surface area of the given two spheres is 16 : (17)⅔

If Correct Question :-

The volume of two spheres are in the ratio 64 : 27. Find the ratio of their surface area.

Then the ratio can be calculated following the above procedure. So, In this case, Our answer would be.

Ratio of radius :-

⇒ (4/3 πR³) / (4/3 πr³) = 64 / 27

⇒ R³ / r³ = 64 / 27

⇒ R / r = 4 / 3

Now, Putting this in the following expression to get the ratio.

⇒ 4πR² / 4πr²

⇒ R² / r²

⇒ (4/3)²

⇒ 16 / 9

Now, The ratio would be 16 : 9