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
Mid circle radius
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.

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About mvtrinh

Retired high school math teacher.
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