Question

A solid consist of a cylinder fitting right circular cone placed on top the height is h vol of solid 3times the vol of cone then find its height

Answer 1

let both have radii r . and height of cylinder = H

a/c to question,
volume of solid =3 volume of cone
π r^2 H+ πr^2h/3 =3 π r^2 h/3
H + h/3 = h
H =2h/3

it means height of cylindrical part is 2/3 times of height of conical part .

Answer 2

Let r be the radius of the cylinder and cone be r. 
H be the height of cylinder respectively.
We know,
Volume of cone + Volume of cylinder = total volume of solid
⇒1/3πr²h + πr²H = 3×1/3πr²h
⇒1/3πr²h + πr²H = πr²h
⇒2/3πr²h = πr²h
⇒H = 2/3h
∴ Height of cylinder = 2/3h