OpenStudy (anonymous):

An aquarium sells cubic fish tanks of different sizes. The length of the small size fish tank is 4 feet. The dimensions of the jumbo size fish tank are double the dimensions of the small size fish tank. Which expression can be used to find the ratio of the volume of the small size fish tank to the volume of the jumbo size fish tank?

6 years ago
OpenStudy (anonymous):

8/4^2 4/8^3 8/4^3 4/8^2

6 years ago
OpenStudy (nikolas):

The volume of a cube is equal to the product of its length, width, and height - all of which I'm assuming are four feet in this case. So the volume of the first cube is 4^3 = 64 cubic feet. You can find the volume of the second cube in the same way (just double the length from four feet to eight feet) and when you divide the smaller number by the larger number you should be able to reduce to one of those answers.

6 years ago
OpenStudy (anonymous):

so it would be 8^3 for volume of larger fish tank?

6 years ago
OpenStudy (nikolas):

Yes, that's right.

6 years ago
OpenStudy (anonymous):

so would the answer be "B"?

6 years ago
OpenStudy (anonymous):

@Nikolas ??

6 years ago
OpenStudy (nikolas):

By B you mean 4/8^3 ? Not quite, think about the ratio you have. If the first volume is 64 and the second volume is 512 (8^3), you need a number that is equal to 64/512. Can you reduce 64/512 to a simpler form?

6 years ago
OpenStudy (anonymous):

1/8?

6 years ago
OpenStudy (nikolas):

That's correct, and I'm not sure why that isn't one of your options, but there is an option there that has the same value as 1/8.

6 years ago
OpenStudy (anonymous):

D?

6 years ago
OpenStudy (nikolas):

Close... but 4/8^2 is 4/64, which works out to 1/16 when you divide both numbers by 4. Your answer should be a choice that gives a value of 1/8 when you divide both numbers by 8.

6 years ago
OpenStudy (anonymous):

omgomgomgomgomg ok! im going with c......

6 years ago
OpenStudy (nikolas):

Haha, you got it :) It's a little tricky, 1/8 like you said would be the simplest answer, but I guess they put in the others to try and throw you off. You can always double-check with a calculator that both the answer and the number you calculated both equal 1/8, just keep in mind that a calculator shouldn't be a replacement for genuine understanding. As long as you know that a cube is equal to the product of its length, width, and height, you should be fine for any other problems like this :)

6 years ago
OpenStudy (nikolas):

*the volume of a cube, that is

6 years ago
OpenStudy (anonymous):

alright thanks for the help! apperacite it

6 years ago
OpenStudy (nikolas):

No problem :)

6 years ago