Question

Two cones are similar. The volume of the larger cone is 27 cm' and the volume of the smaller

cone is 8 cm". The height of the smaller cone is 2 cm.
What is the height of the larger cone?

Answer 1

3

Explanation:

Let V and v be volumes of two similar cones.

so R/r=H/h

V=1/3π R²H

v=1/3πr²h

`(V)/(v) =(\pi R^2H )/(\pi r^2h ) =((R)/(r) )^2((H)/(h) )=((H)/(h) )^3\\(27)/(8) =((H)/(2) )^3\\(3^3)/(2^3) =((H)/(2) )^3\\((3)/(2) )^3=((H)/(2) )^3\\(H)/(2) =(3)/(2) \\H=(3)/(2) * 2=3`