Question

a sphere is melted and recast into a hemisphere show the surface area of the ratio of the surface area of sphere to that of hemisphere is 4:3 3^4​

Answer 1

Answer:

Given : A sphere is melted and recast into a hemisphere.

To Find :  ratio of surface area of sphere to that of hemisphere

Solution:

Let say Radius of Sphere = R

Then Volume = (4/3)πR³

Surface area of sphere = 4πR²

recast into a hemisphere radius = r

=> Volume =  (2/3)πr³

Surface area  of hemisphere  = 3πr²

Volume of both would be same

(2/3)πr³ =  (4/3)πR³

=>r³ = 2R³

=> r = ∛2 R

Surface area of hemisphere  = 3πr²    = 3π ( ∛2 R)²

=  3π∛4 R²

Surface area of sphere / surface area of hemisphere =  4πR² /  3π∛4 R²

= 4 : 3 ∛4  

ratio of surface area of sphere to that of hemisphere  = 4 : 3 ∛4  

Step-by-step explanation: