The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the original one.
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Answers
Step-by-step explanation:
Given:-
The radius of the base of a right circular cylinder is halved and the height is doubled.
To find:-
What is the ratio of the volume of the new cylinder to that of the original one.
Solution:-
Let the radius of the base of a right circular cylinder be 'r' units
and it's height be 'h' units
Volume of a cylinder = πr^2h cubic units
V1 = πr^2h cubic units -----------(1)
Now if the radius is halved then the radius of the new cylinder = r/2 units
If the height is doubled then the height of the new cylinder =2h units
Volume of the new cylinder =
V2 = π(r/2)^2×(2h) cubic units
=>V2 = π×(r^2/4)×2h
=>V2 = π×r^2×2h/4
=>V2 = πr^2h/2 cubic units----------(2)
Ratio of the volume of new cylinder to the original cylinder = V2:V1
=>πr^2h/2 : πr^2h
=>(πr^2h/2)/(πr^2h)
=>(1/2):1
=>1:2
Ratio = 1:2
Answer:-
Ratio of the volume of new cylinder to the original cylinder = 1:2
Used formulae:-
- Volume of a cylinder = πr^2h cubic units
Refer to the attachment please.
