YoungKukie24
28.01.2020 •
Mathematics
The height of one solid limestone square pyramid is 12 m. a similar solid limestone square pyramid has a height of 15 m. the volume of the larger pyramid is 16,000 m3. determine each of the following, showing all work and reasoning.
(a) the scale factor of the smaller pyramid to the larger pyramid in simplest form
(b) the ratio of the area of the base of the smaller pyramid to the larger pyramid
(c) ratio of the volume of the smaller pyramid to the larger
(d) the volume of the smaller pyramid
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Ответ:
Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is
Part b) The ratio of the area of the base of the smaller pyramid to the larger pyramid is
Part c) The ratio of the volume of the smaller pyramid to the larger pyramid is
Part d) 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) The ratio of the area of the base of the smaller pyramid to the larger pyramid
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
Let
z----> the scale factor
x----> the area of the base of the smaller pyramid
y----> the area of the base of the larger pyramid
we have
substitute
Rewrite
-----> ratio of the area of the base of the smaller pyramid to the larger pyramid
Part c) 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 d) 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 and solve for x
Ответ:
Using the t-distribution, it is found that the appropriate critical value is t = 2.9208.
The standard deviation for the population is unknown, hence, the t-distribution is used.
To find the critical value, two parameters are needed.
The confidence level.The number of degrees of freedom(df), which is one less than the sample size.For this problem, there is a confidence level of 99% and 17 - 1 = 16 df, hence, using a t-distribution calculator, the critical value is t = 2.9208.
A similar problem is given at link