Question

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

Answer 1

Answer:

The ratio of cylinder, cone and hemisphere is 3 : 1 : 2.

Step-by-step explanation:

Given :  

Base of a Cylinder , cone and a hemisphere are equal then their Radius are also equal.

Radius and heights of the Cylinder , cone and a hemisphere are same.

Let the radius of the Cylinder = Radius of cone Radius of hemisphere = r

Height of the cone & Cylinder , h =  radius of the hemisphere =  r

Let the volume of cylinder ,cone and hemisphere be V1, V2 & V3.

V1 : V2 : V3 = πr²h : ⅓ πr²h : ⅔ πr³

V1 : V2 : V3 = r²(r) : ⅓ r²(r) : ⅔ r³

V1 : V2 : V3 = r³ : ⅓ r³ : ⅔ r³

V1 : V2 : V3 = 1 : ⅓ : ⅔  

V1 : V2 : V3 =  3 : 1 : 2

Volume of cylinder : Volume of cone : Volume of hemisphere = 3 : 1 : 2

Hence, the ratio of cylinder cone and hemisphere is 3 : 1 : 2.

HOPE THIS ANSWER WILL HELP YOU…..

Answer 2

SOLUTION

=Volume of cone= (1/3)πr^2

=Volume of hemisphere= (2/3)πr^3

=Volume of Cylinder= πr^2h

=) Given that cone, Hemisphere and cylinder have equal base and same height That is r=h

=) volume of cone: volume of Hemisphere: volume of Cylinder= (1/3)πr^2h:(2/3)πr^3: πr^2h

=) (1/3)πr^3: (2/3)πr^3:πr^3

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

=) 1:2:3 [answer]

Hope it helps