Question

Find the ratio of volume of cylinder. When the radius is halved, and the height is same to that of volume of cylinder.​

Answer 1

$\mathcal{SOLUTION-}$

Let,

Radius - r

Height - h

New Dimensions,

Radius - $\frac{r}{2}$

Height - h

$\boxed{Volume\:of\:cylinder=\pi\:r^{2}h}$

Comparing the volumes,we get

$\frac{\pi{\frac{r^{2}}{4}}h}{\pi\:r^{2}h}$ (r²/4 because r is squared so 2² = 4)

= $\frac{1}{4}$

Ratio - 1:4

Answer 2

Hope you would like it..

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Volume of cyllinder=πr²h

hence we can say that if height remains same ,then volume is directly proportional to square of radius of cyllinder

Hence V1/V2 = (r1)²/(r2)²

or, V1/V2 = (r1)²/(r2)²

or , V1/V2 =[(r1/r1)*2]²

:{since r2= r1/2}

or , V1/V2 =4

or v1 = 4V2

Volume of cylinder will be quarter of initial volume if the radius is halved, and the height is same .

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Good luck!!