Question

If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of the original?​

Answer 1

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$\huge\mathcal\pink{Solution:-}$

☘ Answer:-

1 : 4

☘ Step-by-step explanation:-

Let r be the radius of the base and h be the height of the given cylinder.

As per the condition given, radius of the base and the height of the reduced cylinder are r/2 and h respectively.

Now,

Let V1 and V2 be the volumes of the given cylinder and reduced cylinder respectively.

Then,

V1 = πr²h cubic units and,

V2 = π [r/2]²h = π/4 r²h cubic units.

=> V1/V2 = πr²h/π (r²/4)h = 4 => V2/V1 = 1/4

☞ V2 : V1 = 1:4

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Answer 2

Let r be the radius of the base and h be the height of the given cylinder.

Let r be the radius of the base and h be the height of the given cylinder.As per the condition given, radius of the base and the height of the reduced cylinder are r/2 and h respectively.

Now,

Let V1 and V2 be the volumes of the given cylinder and reduced cylinder respectively.

Then,

V1 = πr²h cubic units and,

V2 = π [r/2]²h = π/4 r²h cubic units.

=> V1/V2 = πr²h/π (r²/4)h = 4 => V2/V1 = 1/4

 V2 : V1 = 1:4