Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. What is the ratio of their volumes?

Answer 1

Answer:

Ratio of their volumes is V1 : V2 : V3 = 1: 2: 3

Step-by-step explanation:

SOLUTION :  

Given :  Cone, hemisphere and cylinder have equal base and same height, i.e h = r  

Volume of cone,V1 : Volume of hemisphere ,V2 : Volume of cylinder ,V3

V1 : V2 : V3 = (1/3)πr²h :  (2/3)πr³ : πr²h

= (1/3)πr² (r) :  (2/3)πr²(r) : πr²(r)

= (1/3)πr³ :  (2/3)πr³ : πr³

= (1/3) : (2/3) : 1

Multiplying by 3  

V1 : V2 : V3 = 1: 2: 3

Hence, Ratio of their volumes is V1 : V2 : V3 = 1: 2: 3

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

AS THEY ARE ON SAME BASE AND HAVE SAME HEIGHT.

AS BASE IS SAME THE RADIUS WILL ALSO BE SAME.

CONE :

VOLUME:: 1/3πR^2H

HEMISPHERE:

VOLUME::2/3πR^3

THE RADIUS OF THE FIGURES WILL BE EQUAL TO THEIR HEIGHT AS HEIGHT AND RADIUS OF A HEMISPHERE ARE EQUAL.

CYLINDER:

VOLUME::πR^2H

RATIO:

(1/3πR^2H)/(2/3πR^3)/(πR^2H)

=1/3:2/3:1