Question

A small rectangular prism is 4 inches long. A large rectangular prism is 24 inches long. These two prisms are similar. Which statement is true and why.
a. The volume of the large rectangular prism is 6 times the volume of the small one.
b. The volume of the large rectangular prism is 20 times the volume of the small one.
c. The volume of the large rectangular prism is 36 times the volume of the small one.
d. The volume of the large rectangular prism is 216 times the volume of the small one.
The correct answer is D according to the key but I cannot figure out how to prove it or even get that answer. I thought it was A also.

Answer 1

It is just comparing the ratio of both, which we can find by dividing the larger length by the smaller length.

\[\frac{24}{4} = ?\]

Answer 2

The answer key says 216 times the volume. I thought is was 6 also.

Answer 3

I got his wrong and have to prove the correct answer but I do not know how to get to 216.
as the correct answer.

Answer 4

I have no idea why the answer is D . . . o_o

Answer 5

I will ask the teacher I think the Key is wrong. Thanks.

Answer 6

the ratio you have calculated is the LINEAR ratio - i.e. the ration of 1 length

BUT

the prism expands in ALL THREE axes by a factor of 6

SO the VOLUME ratio is 6*6*6 = 216

Answer 7

IS this really 7th grade pre algebra? Seems really hard.

Answer 8

just imagine a cube (which is type of prism) of side 1"

If you scale it by 6x and keep the shape 'similar' then each side is 6"

the volume of a cube is the length cubed - so in th efirst case it is 1 cu in, in th second it is 216

Answer 9

I am a SPED teacher and am trying to prepare my daughter for state testing. I am posting the questions she missed and cannot answer so that I can explain and she can work some similar problems. They gave me a key but no explanations. I believe in show your work.

Thanks.
April

Answer 10

She will be taking Algebra in 8th grade and is an honor student. I think I need to look for a tutor. :as I am way behind the times. My students are just learning to use a calculator.
LOL

Answer 11

the volume of ANY prism is the area of the end times the height of the prism.

If you increase the size by a factor then you can see that the area increases by the factor squared, and the height by the factor. Therefore the volume increases by facor cubed

Answer 12

That makes perfect sense. Thanks so much.

Answer 13

at least you've grasped the calculator, and not stuck with the slide rule