Question

The volume of the two spheres are in the ratio 64:27.Find the difference of their surface areas if the sum of their radii is 7

Answer 1

If the volume of two spheres are in the ratio is 64:27, then what is the ratio of their surface area?

The volume of a sphere is given by

V=43πr3V=43πr3

and it's total surface area is given by

AT=4πr2AT=4πr2

Where, rr is the radius of the sphere.

Let the volume of two spheres, say S1S1and S2S2, be V1V1 and V2V2, that are in the ratio is 64:27.

⇒V1:V2=64:27⇒V1:V2=64:27

⇒V1V2=43πr3143πr32=6427⇒V1V2=43πr1343πr23=6427

⇒r31r32=6427⇒r13r23=6427

⇒r31r32=4333⇒r13r23=4333

⇒r1r2=43⇒r1r2=43

Then the ration of the total surface area of the two spheres will be:

AT1AT2=4πr214πr22=4232AT1AT2=4πr124πr22=4232

⇒AT1:AT2=16:9