Question

Volumes of two spheres are in the ratio 64:27, then find the ratio of their surface areas.​

Answer 1

vol of sphere =4\3πr^3

implies 64\27

the ratio f radius is 4\3

surface area of sq = 4πr^2

ratio 16\9

Answer 2

Answer:

16:9

Step-by-step explanation:

HEY MATE HERE'S YOUR ANSWER!

Given, ratio of volumes of two spheres= 64:27

But volume of a sphere= 4/3×π×r^3

•°• A. T. Q,

(4/3×π×(r1)^3)/(4/3×π×(r2)^3) = 64/27, taking radius of sphere 1 as r1 and the other sphere as r2.

==> (r1)^3/ (r2)^3 = 64/27

Taking cube root on both sides, we get-

==> r1/r2 = 4/3

Squaring on both sides,

==>( r1)^2/( r2) ^2 = 16/9 ... eq. 1

Let surface area of sphere 1 be S1 and that of other sphere is S2,

Now,ratio of their surface areas= (4π×(r1)^2)/ (4π×(r2)^2)

==> S1:S2 = (r1)^2/(r2)^2

= 16/9 [From eq. 1]

=16:9

THUS THE RATIO OF THEIR SURFACE AREAS IS 16:9.

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