Question

10. A cone, a hemisphere and a cylinder stand on equal bases and have the same height equal to the radius of the bases of these solids. Show that their volumes are in the ratio 1:2:3.​

Answer 1

Answer:

Complete step-by-step answer:

As the height and radius of cylinder, cone and hemisphere are the same.

So, let their height be h units.

And their radius is r units.

Now as we know that the height of the hemisphere is the radius of the hemisphere.

So, r = h (because h is the height of all shapes and r is the radius of all shapes)

So, as we know that if h is the height and r is the radius of cylinder then its volume is calculated as πr2h

Let the volume of the cylinder is V1

.

So, V1=πr2h=πr3

(because h = r)

As we know that if h is the height and r is the radius of cone then its volume is calculated as 13πr2h

Let the volume of the cone is V2

.

So, V2=13πr2h=13πr3

(because h = r)

As we know that if r is the radius of hemisphere then its volume is calculated as 23πr3

Let the volume of the hemisphere is V3

.

So, V3=23πr3h

Now the ratio of the volumes of cylinder, cone and hemisphere is the ratio of V1

, V2

and V3

.

So, V1:V2:V3=πr3:13πr3:23πr3=1:13:23

On multiplying ratio be 3. We get,

V1:V2:V3=3:1:2

Hence, the volume of the cylinder cone and hemisphere are in ratio 3 : 1 : 2.

Answer 2

ratio 1.2.3 intangible off questions of solids