Question

An aquarium sells cubic fish tanks of different sizes. The length of the small size fish tank is 2 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?

(2/4)^2
(2/4)^3
(4/2)^2
(4/2)^3

Answer 1

@phi I eliminated b and d, but im stuck on this question.

Answer 2

you want the ratio of
volume of small/ volume of large

First,
what do you know about the volume of the small? it is *cubic* what does that mean ?

Answer 3

to the third power

Answer 4

cubic does mean to the 3rd power, but when we are talking about a geometric object, it means a cube: length=width= depth a "cube" is like a 3-D version of a square.

that means you if you know its length, you also know its width and height.

Answer 5

Okay.

Answer 6

volume of a prism is V= L*W*H or in this case V (small cube)= 2*2*2 = 2^3

now the jumbo size fish tank are double the dimensions of the small size fish tank.
what does that mean its dimensions are ?

Answer 7

4*4*4=4^3?

Answer 8

yes, and the ratio (fraction) of the volume of the small tank over the volume of the humongous tank is ?

Answer 9

you should get
\[ \frac{2^3}{4^3} = \frac{2 \cdot2\cdot 2}{4\cdot4\cdot4} = \frac{2}{4} \cdot \frac{2}{4} \cdot \frac{2}{4} = \left( \frac{2}{4}\right)^3\]

of course, they could have simplified this to
\[ \left(\frac{1}{2}\right)^3 \]
or even
\[ \frac{1}{8} \]