Question

(h) The height of one solid limestone square pyramid is 24 m. A similar solid limestone square pyramid has a height of 30 m. The volume of the larger pyramid is 16,000 m3. Determine each of the following, showing all your 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
(i) The volume of the smaller pyramid

Answer 1

Please Help

Answer 2

@soprano.h.d0816

Answer 3

@izze17

Answer 4

@Tennis5518

Answer 5

sry idk

Answer 6

@izze17 its ok

Answer 7

@Yuliacosta111

Answer 8

sorry idk

Answer 9

can you come back for help - i can give you

Answer 10

@jhonyy huh?

Answer 11

have you tried anything yet?

Answer 12

ok i see

Answer 13

You need to find the scale factor.
You know that a side measuring 24 m corresponds to a side measuring 30 m.
What is the scale factor of the side lengths?

Answer 14

@Error1603 yes i have.. and i need to learn how to do it, i tried asking my teacher last week she never got back to me

Answer 15

its not a or d

Answer 16

@mathstudent55 thescale factor is 4/5

Answer 17

should say i

Answer 18

@math_man21 its not multiple choiceis free response .

Answer 19

Great. Since 24/30 = 4/5 = 0.8
That is correct.
You have answered part (a)

Answer 20

oh i see what we are doing now

Answer 21

Now let's look at part (b).
We are dealing with two square prisms.
That means the bases are squares.
Let's say the base of the larger prism measures L by L.
Since the scale factor is 0.8, what does the base of the smaller prism measure?

Answer 22

Since the scale factor is 0.8, and the length and width of the larger prism are both L, what are the length and width of the base of the smaller prism?

Answer 23

@mathstudent55 so how would I find the base of the smaller prism?
do I ned to divide 16,00 by 30

Answer 24

No.
Please just answer my question.
The prisms have a scale factor of 0.8
Every linear dimension in the smaller prism is 0.8 the size of the corresponding dimension in the larger prism.
If a measure is L in the larger prism, what is it in the smaller prism?
(Hint: use L and the scale factor.)

Answer 25

Hint 2:
We know the heights are 30 m and 24 m.
What do you multiply 30 m by to get 24 m?

Answer 26

ohhh you would multilply 30m by 0.8 to get 24m

Answer 27

@mathstudent55

Answer 28

Correct. If you multiply 30 m by 0.8 to get 24 m because 0.8 is the scale factor, you multiply every linear dimension by 0.8 also.
If the dimensions of the base (length and width) are both L in the larger prism, then in the smaller prism the length and width are both 0.8L
Ok?

Answer 29

Now we can answer part (b).
What is the ratio of the area of the smaller base to the larger base?
Small base: square with side 0.8L
Large base: square with side L
You have the sides of two squares. Find their areas and divide the smaller area by the larger area. Leave the result as a reduced fraction since they want a ratio.

Answer 30

so in order for me to find the area i would multiply 24 times 0.8 for the small base and 30 times ..... what for the larger one

Answer 31

@mathstudent55

Answer 32

No.
24 m is the height. It has nothing to do with the area of the base.
The base of the larger prism is a square that measures L by L.
Forget the rest of this problem for a moment.
Here is a simple question.
If the side of a square has length L, what is the area of the square?

Answer 33

L times L

Answer 34

Correct. The area is L^2
The larger prism has a base shaped like a square.
Its side measures L.
The area of the base of the larger prism is L^2

Answer 35

The smaller prism also has a square as its base.
We already concluded above that the sides of the base of the smaller prism measure 0.8L
What is the area of a square with a side of length 0.8L?

Answer 36

.64l times L

Answer 37

\(A_{square} = s^2\)

Square with side L:

\(A = L^2\)

Square with side 0.8L:

\(A = (0.8L)^2 = 0.8^2 \times L^2 = 0.64L^2\)

Answer 38

Right.
The area of the small base is 0.64L^2
The area of the large base is L^2

Now we need the ratio of the small area tot eh large area:

\(\dfrac{0.64L^2}{L^2}\)

You can cancel the L^2 in the numerator and denominator.
What is the ratio of the bases of the small prism to the large prism?

Answer 39

.64

Answer 40

Correct. The ratio is 0.64 to 1
We can write it as:

\(\dfrac{0.64}{1} = \dfrac{64}{100} = \dfrac{16}{25} \)

Answer 41

Now notice this.
The ratio of the sides is 4/5, remember that?

Answer 42

Yes

Answer 43

What is the ratio of the areas? We just found out it is 16/25
Do you notice that the ratio of the areas is the square of the ratio of the sides?
16/25 is the square of 4/5

Answer 44

ohh ok I see

Answer 45

Now we can do part (c)
The volume of a prism is area of the base times height.

Large Prism Base Area: L^2 Small prism Base area: 0.64L^2
Large prism height: 30 m Small prism height: 0.8(30 m)
Volume: L^2 * 30 m Volume: 0.64L^2 * 0.8(30 m)

Ratio of volumes (smaller to larger):

\(\dfrac{0.64L^2 \times 0.8(30 ~m)}{L^2 \times 30 ~m} \)

\(\dfrac{0.64\cancel{L^2} \times 0.8(\cancel{30 ~m})}{\cancel{L^2} \times \cancel{30 ~m}~~1} \)

\(= \dfrac{0.64 \times 0.8}{1}\)

\(=\dfrac{0.512}{1}\)

\(=\dfrac{512}{1000} = \dfrac{64}{125} \)

The ratio of the volumes is the cube of the scale factor.

\((\dfrac{4}{5})^3 = \dfrac{64}{125} \)

Answer 46

Since the ratio of the volumes is 0.512/1, just multiply the volume of the larger prism by 0.512 to find the volume of the smaller prism. That is what part (d) asks.

Answer 47

Sorry, but gtg.
Bye

Answer 48

@mathstudent55 thnks!

Answer 49

You're welcome.