Question

A cylinder a cone and a hemisphere are of equal base and have the same height what is the ratio of their volumes ? please tell this answer with crt explanation​

Answer 1

Answer:

The required ratio of the volumes is 3 : 1 : 2

Step-by-step explanation:

Given :

A cylinder, a cone and a hemisphere are of equal base and have the same height.

To find :

the ratio of their volumes

Solution :

Let the radius be 'r' and height be 'h'

• Volume of cylinder =  $\bf \pi r^2h$

• Volume of cone =  $\bf \dfrac{1}{3} \pi r^2h$

• Volume of hemisphere =  $\bf \dfrac{2}{3} \pi r^3$

We have to find the ratio of their volumes.

⇒ Volume of cylinder : Volume of cone : Volume of hemisphere

$\implies \sf \pi r^2h:\dfrac{1}{3} \pi r^2h : \dfrac{2}{3} \pi r^3 \\\\ \implies \sf \pi \not{r^2} h:\dfrac{1}{3} \pi \not{r^2}h : \dfrac{2}{3} \pi \not{r^3} \\\\ \implies \sf \pi h:\dfrac{1}{3} \pi h : \dfrac{2}{3}\pi r \\\\ \implies \sf \not{\pi} h:\dfrac{1}{3} \not{\pi} h : \dfrac{2}{3} \not{\pi} r \\\\ \implies \sf h:\dfrac{h}{3}:\dfrac{2r}{3}$

In case of hemisphere, r = h

$\implies \sf \not{h} :\dfrac{\not{h}}{3} : \dfrac{2\not{h}}{3} \\\\ \implies \sf 1:\dfrac{1}{3} : \dfrac{2}{3} \\\\ \implies \sf \dfrac{3}{3} : \dfrac{1}{3} : \dfrac{2}{3} \\\\ \implies \sf \dfrac{3}{\not{3}} : \dfrac{1}{\not{3}} : \dfrac{2}{\not{3}} \\\\ \implies \bf 3:1:2$

Therefore, the required ratio of the volumes is 3 : 1 : 2

Answer 2

Answer:

above answer is correct thanks for the question