Question

A wooden pyramid, 6 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 3 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids. i know the ratio is 1/6 but im not sure how to explain everything??

Answer 1

?? can anyone help me

Answer 2

the ratio of the linear measurements is 1:3 the ratio of volumes can be found by raising each value in the ratio to the power of 3 (1)^3 :(3)^3 = 1:27 a test.... height 6 and assume the square base has side length of 1 inch
V=1/3×12×6
V = 2 inches^3 now with the dimensions tripled h = 18 and square side length is 3
V=1/3×32×18
V = 54 inches ^3 the ratio of the volumes is 2:54 or 1: 27

Answer 3

thnk u

Answer 4

no i i get it

Answer 5

how do u get 1/3

Answer 6

It's increasing by a factor of three... meaning that it's growing three times bigger not six. Therefore, for every one dimension it's increasing by itself 3 times. Make sense?

Answer 7

yea

Answer 8

so like multiplying right

Answer 9

kind of...

Answer 10

oh

Answer 11

how do you know whaT to multiply by when ur calculating everything

Answer 12

Well I'm going to answer your question with a question.. How did you get 6?

Answer 13

i had guessed because you were starting of with 6 inches

Answer 14

The way I think about it is basically if you started at 1 inch and it grew 3 more inches then it would be a ratio of 1/3

Since it starts with 6 and grow three times it would be 6/18 and then you can simplify that into 1/3

Answer 15

oh

Answer 16

but i thought that u said it was 1/3

Answer 17

so 1/3 is just the simplified ratio?

Answer 18

no. if someone were to look at this and have to figure out the ratio without any math they would easily get 1/3. I see where you got 1/6 though.

Answer 19

oh

Answer 20

Get it now?

Answer 21

yes lol i was so confused

Answer 22

thank u so much

Answer 23

Anytime! :)

Answer 24

wait when you were mutpliying 1/3x12x6 how did u get the 12