Question

10. Height of a cyl
cylinder
HOTS
11. If the radius of a cylinder is doubled, what will be the ratio between the volume of the new
cylinder to the volume of the original one?
7 If radius and height both are doubled, find the ratio between the volumes of the new with the
\uots)​

Answer 1

$\text{\large\underline{\orange{Solution:}}}$

$\underline{\bigstar\:\textsf{Let's\:analyze\:the\:given\:conditions\:!}}$

(i) If the radius of a cylinder is doubled (if r = 2r), then what will be the ratio between the volume of the new cylinder (V') to the volume of the original one (V) ?

(ii) If the radius and height both are doubled means if r = 2r and h = 2h, then what will be the ratio between the volume of the new cylinder (V') to the original one (V) ?

$\underline{\bigstar\:\textsf{Let's\:find\:now\:!}}$

(i) $\blue{Volume\:of\:cylinder\:=\:\pi\:r²h}$

$\implies$ V' = $\pi$ (2r)²h

$\implies$ V' = $\pi$ 4r²h

And our original volume was $\pi r²h$

$\implies\dfrac{V'}{V}\:=\:\dfrac{\pi\:4r²h}{\pi\:r²h}$

$\implies\dfrac{V'}{V}\:=\:\dfrac{4r²}{r²}$

$\implies\dfrac{V'}{V}\:=\:\dfrac{4}{1}$

${\large{\boxed{\sf{\therefore \:V':V\:=\:4:1}}}}$

(ii) r = 2r and h = 2h

$\implies$ V' = $\pi\:\times\:(2r)²\:\times\:(2h)²$

$\implies$ V' = $\pi\:4r²\:\times\:4h²$

$\implies\dfrac{V'}{V}\:=\:\dfrac{\pi\:4r²4h²}{\pi\:r²h}$

$\implies\dfrac{V'}{V}\:=\:\dfrac{4\:×\:4h}{1}$

$\implies\dfrac{V'}{V}\:=\:\dfrac{16h}{1}$

${\large{\boxed{\sf{\therefore \:V':V\:=\:16h:1}}}}$

Hope it helped you dear...