Mathematics, 28.01.2020 22:08 pcastaneda03

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

Answers: 3

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Answer from: live4dramaoy0yf9

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is $\frac{4}{5}$

Part b) The ratio of the area of the base of the smaller pyramid to the larger pyramid is $\frac{16}{25}$

Part c) The ratio of the volume of the smaller pyramid to the larger pyramid is $\frac{64}{125}$

Part d) The volume of the smaller pyramid is $8,192\ m^{3}$

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

Let

z----> the scale factor

x----> the height of the smaller pyramid

y----> the height of the larger pyramid

$z=\frac{x}{y}$

substitute the values

$z=\frac{12}{15}$

Simplify

$\frac{12}{15}=\frac{4}{5}$ -----> 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

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

$z^{2} =\frac{x}{y}$

we have

$z=\frac{4}{5}$

substitute

$(\frac{4}{5})^{2} =\frac{x}{y}$

$(\frac{16}{25})=\frac{x}{y}$

Rewrite

$\frac{x}{y}=\frac{16}{25}$ -----> 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

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3} =\frac{x}{y}$

we have

$z=\frac{4}{5}$

substitute

$(\frac{4}{5})^{3} =\frac{x}{y}$

$(\frac{64}{125})=\frac{x}{y}$

Rewrite

$\frac{x}{y}=\frac{64}{125}$ -----> 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

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3} =\frac{x}{y}$

we have

$z=\frac{4}{5}$

$y=16,000\ m^{3}$

substitute and solve for x

$(\frac{4}{5})^{3} =\frac{x}{16,000}$

$(\frac{64}{125})=\frac{x}{16,000}$

x=16,000*64/125

$x=8,192\ m^{3}$

Answer from: Quest

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x.

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

Answer from: Quest

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.

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