The diameter of one sphere is double the diameter of another sphere.If numerical value of T.S.A of larger sphere is equal to the volume of smaller sphere,then find the radius of smaller sphere
Answers
Step-by-step explanation:
Given :-
The diameter of one sphere is double the diameter of another sphere and numerical value of T.S.A of larger sphere is equal to the volume of smaller sphere.
To find :-
Find the radius of smaller sphere ?
Solution:-
Let the diameter of the smaller sphere be d units
Then the radius of the smaller sphere = d/2 units
Then , The diameter of the larger sphere
= Double the diameter of the second sphere
= 2d units
Radius of the larger sphere = 2d/2 = d units
Now ,
Volume of a sphere = (4/3)πr^3 cubic units
Volume of the smaller sphere
= (4/3)×π×(d/2)^3 cubic units
=> (4/3)×π×(d^3/8)
=> (4×π×d^3)/(3×8)
=> (π×d^3)/(3×2)
=> πd^3/6 cubic units --------(1)
Total Surface Area of a sphere=4πr^2 sq.units
Total Surface Area of the larger sphere
= 4×π×d^2 sq.units
=> 4πd^2 sq.units ---------------(2)
Given that
TSA of the larger sphere = Volume of the smaller sphere
=> 4πd^2 = πd^3/6
=> 4πd^2 ×6 = πd^3
=> 24 πd^2 = πd^3
=> 24 ×πd^2 = πd^2 ×d
=> 24 = d
=> d = 24 units
Radius of the larger sphere = 24 units
Radius of the smaller sphere = d/2 units
=> 24/2
=> 12 units
Answer:-
The radius of the smaller sphere for the given problem is 12 units
Used formulae:-
- Radius = Diameter/2
- Total Surface Area of a sphere=4πr^2 sq.units
- Volume of a sphere = (4/3)πr^3 cubic units