Question

if the diameter of a cylinder is half then find the ratio between the volume of new and the old one

Answer 1

let diameter is x
and volume is 1
the ratio is x:1

Answer 2

Hey mate..
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Given,

Diameter of the new cylinder = d/2

Thus,

Radius of the new cylinder = 1/2 × d/2 = d/4

Now,

Volume of the new cylinder with that of the old cylinder

= $\frac{ \frac{1}{3}\pi \: r {}^{2} h }{ \frac{1}{3} \pi \: r {}^{2} h}$

= $\frac{ \frac{1}{3} \pi( \frac{d}{4}) {}^{2}h }{ \frac{1}{3} \pi \: ( \frac{d}{2} ) {}^{2} h}$

= $\frac{ \frac{d {}^{2} }{16} } { \frac{d {}^{2} }{4} }$

= $\frac{4}{1}$

= 4 : 1

#racks