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

Answer:

3

Step-by-step explanation:

Let V and v be volumes of two similar cones.

so R/r=H/h

V=1/3π R²H

v=1/3πr²h

$\frac{V}{v} =\frac{\pi R^2H }{\pi r^2h } =(\frac{R}{r} )^2(\frac{H}{h} )=(\frac{H}{h} )^3\\\frac{27}{8} =(\frac{H}{2} )^3\\\frac{3^3}{2^3} =(\frac{H}{2} )^3\\(\frac{3}{2} )^3=(\frac{H}{2} )^3\\\frac{H}{2} =\frac{3}{2} \\H=\frac{3}{2} \times 2=3$