An engineer studying fuel usage collected data on the speed a car traveled (in kilometers per hour) and how much fuel it used (i
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Answer:
Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is
Part b) The ratio of the volume of the smaller pyramid to the larger pyramid is
Part c) The volume of the smaller pyramid is
Step-by-step explanation:
Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form
we know that
If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor
so
Let
z----> the scale factor
x----> the height of the smaller pyramid
y----> the height of the larger pyramid
substitute the values
Simplify
-----> scale factor in simplest form
Part b) Ratio of the volume of the smaller pyramid to the larger pyramid
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
Let
z----> the scale factor
x----> the volume of the smaller pyramid
y----> the volume of the larger pyramid
we have
substitute
Rewrite
-----> ratio of the volume of the smaller pyramid to the larger pyramid
Part c) The volume of the smaller pyramid
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
Let
z----> the scale factor
x----> the volume of the smaller pyramid
y----> the volume of the larger pyramid
we have
substitute the values and solve for x