Question

hi there

A cylinder and cone have base of equal radii and are of equal heights. Show that their volumes are in the ratio of 3 : 1.

Answer 1

here is ur answer.......

Answer 2

ANSWER -

Question -

A cylinder and cone have base of equal radii and are of equal heights. Show that their volumes are in the ratio of 3 : 1.

Now

Solution-

Given

radius of cylinder=radius of cone

height of cylinder= height of cone.

To prove-

Show that their volumes are in the ratio of 3 : 1.

$\bf{ \frac{volume \: of \: cylinder}{volume \: of \: cone} = \frac{ \: \pi \: r ^{2} h}{ \frac{1}{3} \pi \: r ^{2} h}}$

hence

$\bf{ \frac{volume \: of \: cylinder}{volume \: of \: cone} = \frac{ \not{\pi} \not{\: r ^{2} } \not{h}}{ \frac{1}{ 3} \not{\pi} \not{r ^{2} } \not{h}} }$

$\bf{ \frac{volume \: of \: cylinder}{volume \: of \: cone} = \frac{1}{ \frac{1}{3}} }$

$\bf{ \frac{volume \: of \: cylinder}{volume \: of \: cone} = \frac{3}{1}}$

hence

it is proved that

ratio of volumes= 3:1


Hope it helps

thanks