Volume of two spheres are in the ratio 64 is to 27 the ratio of their surface areas is

Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is 16:9.

Explanation:

Let the radii of the two spheres are r1 and r2, respectively.

∴ Volume of the sphere of radius

r1 = V1 = `43 pir_1^3`   [∵ Volume of sphere = `4/3pi` (radius)3]   ........(i)

And volume of the sphere of radius 

r2 = V2 = `4/3 pi r_2^3`   ......(ii)

Given, ratio of volumes = V1:V2 = 64:27

⇒ `(4/3 pir_1^3)/(4/3 pir_2^3) = 64/27`  ....[Using equations (i) and (ii)]

⇒ `(r_1^3)/(r_2^3) = 64/27` 

⇒ `r_1/r_2 = 4/3`   .....(iii)

Now, ratio of surface area = `(4 pir_1^2)/(4 pir_2^2)`   ......[∵ Surface area of a sphere = 4π (radius)2]

= `r_1^2/r_2^2`

= `(r_1/r_2)^2 = (4/3)^2`   .....[Using equation (iii)]

= 16:9

Hence, the required ratio of their surface area is 16:9.

Distribute the referral code to your friends and ask them to register with Tutorix using this referral code.

Once we get 15 subscriptions with your referral code, we will activate your 1 year subscription absolutely free.

Your subscribed friend will also get 1 month subscription absolutely free.