## Snowman

A family builds a snowman with three perfectly rolled spheres. If the radii of the three spheres are in geometric progression and if the top sphere has a radius of $8$ in. and the bottom sphere has a radius of $18$ in., what is the volume of the entire snowman?

Source: NCTM Mathematics Teacher 2008

SOLUTION
Geometric progression $a,ax,ax^2,\cdots$
$a=8;ax^2=18$
$8x^2=18$
$4x^2=9$
$x^2=9/4$
$x=3/2$
$ax=8(3/2)=12$ in.
Volume of the entire snowman
$(4/3)\pi 8^3+(4/3)\pi 12^3+(4/3)\pi 18^3=(4/3)\pi [8^3+12^3+18^3]$
$= (4/3)\pi (8072)$
$=33811.91$ cubic in.

Answer: $33811.91$ cubic in.