Question

the ratio of 2 spheres' volumes is 64:27. if the sum of their radii is 7cm' find the difference in their surface areas.
the correct answer will be the brainliest

Answer 1

Answer:

28 π

Step-by-step explanation:

Let R be the radius of the larger sphere and r the radius of the smaller sphere.

Volume = 4 π R³ / 3  (for the large sphere),  4 π r³ / 3 (for the small sphere)

So ratio of their volumes is

R³ / r³ = 64 / 27  = 4³ / 3³  =>  R / r = 4 / 3  =>  3R = 4r

We are told R + r = 7, so

3R = 4r  =>  3R = 4 ( 7 - R )  =>  3R = 28 - 4R  =>  7R = 28  =>  R = 4.

Then also r = 3R / 4 = 3.

Difference of surface areas = 4 π R² - 4 π r² = 4 π ( 16 - 9 ) = 28 π