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
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 :)
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
looks like I went the wrong way, go with Damon.
I shrunk the shrunken one.
It was unclear to me which way the scale was supposed to go actually.
To find the scale factor of a rectangular prism whose volume is half the original volume, we can use the formula:
Scale factor = (New Volume) / (Original Volume)
In this case, the new volume is given as half the volume of the iPad Mini, which is equal to 12.561 in^3. So, we need to find the original volume of the iPad Mini to calculate the scale factor.
To find the original volume, we can use the formula for the volume of a rectangular prism:
Volume = length x width x height
However, the dimensions of the iPad Mini are not given in the question. Therefore, we cannot calculate the exact scale factor or the dimensions of the Mini-Mini tablet with the given information. We need the dimensions of the iPad Mini to proceed with the calculation.
Once we have the dimensions of the iPad Mini, we can calculate its volume. Then, by dividing the volume of the Mini-Mini by the volume of the iPad Mini, we can find the scale factor. Using this scale factor, we can determine the dimensions of the Mini-Mini tablet by multiplying the corresponding dimensions of the iPad Mini by the scale factor.