Question

Can someone help me please?

A wooden pyramid, 12 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 5 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids.

Answer 1

Do you know what the volume of a pyramid is?

Answer 2

1/3 (b)(h)?

Answer 3

Yep. So in the first case, what would the volume be? You to to find the ration you divide the new value by the old value right?

Answer 4

To find the ratio*

Answer 5

Well I know the height, but what's the base?

Answer 6

No need. You got

\[v=\frac{ 1 }{ 3 }A*h\]

Answer 7

h=12.

Answer 8

Therefore:

\[v=\frac{ 1 }{3 } * A *12\]

= \[V=4A\]

Answer 9

Now we are given the ara of the base was increased by a factor of 5. In other words, it was multiplied by 5.

Answer 10

So, 20?

Answer 11

Ratios mean you divide, not multiply.

Answer 12

Now I'm confused :(

Answer 13

About?

Answer 14

I thought you said it was multiplied by 5?

Answer 15

Haha, yeah for the new volume. But when you find a ration you divide the new value by the old value.

Answer 16

ratio*

Answer 17

So... what is the ratio of the volumes of the 2 pyramids? o.o

Answer 18

Lol, I don't want to give you an answer :P . I would rather you understand it.

Answer 19

Allright better explanation.

Answer 20

It's a 1/5 ratio right?

Answer 21

Because we scale the pyramid by a factor of 5.

Answer 22

1:5 ratio sorry.

Answer 23

Ignore all the other parts.

Answer 24

I'm seriously so confused it's not even funny! Lol okay so the dimensions are increased by a facor of 5. So you're saying the ratio of the 2 pyramids is 1:5?

Answer 25

Ahh but remember, since this is volume, we cube that 5.

Answer 26

1/5^3

Answer 27

or 1:125 which can also be 1/125.

Answer 28

My head is starting to hurt..so I cube the ratio 1:5? WHAT? Lol you have to break it down for me all at once. I don't do step by step :b

Answer 29

Allright.

Answer 30

The scale factor of the Pyramid is 1:5 right? This can be re-written as 1/5 .

So the ratio would be 1:5 but since we are dealing with volumes, We have to cube that ratio or in other words, 1/5^3 or 1/125.

We can say the New pyramid is 125x more greater than the old pyramid.

Answer 31

Is that the answer or are you waiting for me to answer? Lol I don't know how to do this.

Answer 32

What don't you understand?

Answer 33

I want to try and help :c .

Answer 34

I'm confused on the entire thing lol, I mean I'd like to understand how to get the right answer so I can fully explain my answer in complete sentences but at this point my head is starting to hurt and I just want to finish it. Lol

Answer 35

initial dimensions; height = 12
let the square base have dimensions of 1
so initial volume = 4

new dimensions, multiply lengths by 5
height = 60
square base have sides of 5 .... so area of 25
new volume = (1/3)(25)(60) = 500

volume ratio = 500/4 = 125

does that help?

Answer 36

in general, the rule is that the volume ratio = (length ratio)^3

--> 5^3 = 125

Answer 37

Yes! Thank you both for helping me.. sorry I get confused so easily! I appreciate you both! :)

Answer 38

:)