# Geometry

What is the scale factor of a rectangular prism that s volume is half the original volume?
Pear-Apple scraps their plans for the BigMini and the Lil Mini. They decide to come up with a
product that is half the volume of the iPad Mini. It’s called the Mini-Mini. What scale factor should
they use? What dimensions should the tablet be

The Mini mini is (7.9)(5.3)(0.3)= 12.561 in^3

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1. if the scale factor is s
Like L' = s L
and w' = s w
and h' = s h
then
L'w' h' = s^3 L w h
in other words
volume scales as the cube of the length scale
if the volume of one thing is twice another similar object
then every length measure on the big one is 2^(1/3) = 1.25992105 times the same measurement on the little one :)

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2. let the new sides be 7.9x , 5.3x , and .3x
(7.9x)(5.3x)(.3x) = 1/2(12.561)
x^3 = .5
x = .5^(1/3) = .7937 <---- scale factor

multiply the original dimensions by that factor

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3. looks like I went the wrong way, go with Damon.
I shrunk the shrunken one.

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4. It was unclear to me which way the scale was supposed to go actually.

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