Question

a cylinder a cone and a hemisphere are equal base and have the same height then the ratio of their volumes is​

Answer 1

SOLUTION

Let r & h be the radius of base & height of the cylinder, cone and hemisphere.

We know that, height of hemisphere= radius of the hemisphere

i.e., h= r

=)Volume of cylinder

=πr^2h=πr^2×r= πr^3

=)Volume of cone

=)1/3πr^2h = 1/3πr^2×r = 1/3πr^3

=)Volume of hemisphere

=) 2/3πr^3

=)Volume of cylinder:Volume of cone: volume of hemisphere

$= > \pi {r}^{3} \ratio \frac{1}{3} \pi {r}^{3} \ratio \: \frac{2}{3} \pi {r}^{3} \\ \\ = > 1 \ratio \: \frac{1}{3} \ratio \frac{2}{3} \: \: \: \: \: \: \: (dividing \: by \: \pi {r}^{3} )$

=) 3: 1: 2 (Multiplying by 3)

Thus, the ratio of their volume is 3:1:2

hope it helps ☺️

Answer 2

$\huge\bf{Answer:-}$

• Let M and N be the Radius of base & height of the cylinder.

Using formula:-

• Height of hemisphere = Radius of the hemisphere.

Cylinder:-

$=> Volume = Cylinder$

$=> πr^2h = πr^2 × r = πr^3$

Cone:-

$=> Volume = cone$

$=> 1/3 πr^2h = 1/3 πr^2 × r = 1/3 πr^3$

Hemisphere:-

$=> Volume = hemisphere$

$=> 2/3πr^3$

$\begin{lgathered}=\pi {r}^{3} </p><p>\ratio \frac{1}{3} \pi {r}^{3}\ratio\: \frac{2}{3} \pi {r}^{3}$

$= 1 \ratio \: \frac{1}{3} \ratio \frac{2}{3}$

=> The Ratio be (3: 1: 2)

We need d to Multiply by 3

Hence ,3 : 1 : 2 is the ratio of their Volume.