Help!Math Question?

Question

Can a cube have a volume of exactly 1 gallon? If its possible what would be the length of each side.I'm having the most trouble with this. I'm assuming it is possible since its a question in my math book. If you can figure this out show me how you did it step by step.

Answer 1

ARRGHH! NOOO!

1 gallon = 3785.412 cubic centimeters
the cube-root of 3785.412 is 15.5849 cm

15.58 cm is 6.13 inches, so a box 15.585 cm on a side is 1 gallon. (you can even visualize that as about the size of a gallon milk-jug.)

Think about it people -- 1.5 centimeters is less than 1 inch.
1 cubic inch is a whole lot smaller than a gallon container of milk.

Answer 2

good try, xxbostonlove.

tlbs101 is right, although perhaps too unforgiving. :-)

He does make a good point about estimating the right answer. We can all visualize the size of a gallon of milk, which, while not a cube, isn't that far off.

Notice how he converted the gallon measurement to cubic centimeters (1000 cc = 1 liter), because it is so much easier to determine how many centimeters would be on each side of a cube in the metric system. (one liter is a cube 10 cm on each side. 10cm x 10cm x 10cm=1000 cubic centimeters, also sometimes called milliliters because each is also 1/1000 of a liter)

Once he knew the number of liters in a gallon (easy to look up), he could multiply by 1000 to get cubic centimeters, (1000 cc in a liter), then squash those liters into a cube, exactly so many cm on a side. (each side would be the cube root of the volume in length, since a cube's volume is given by (length of a side)^3)

hope that additional explanation was helpful. :-) fun problem! And, steph, you were smart to ascertain that at this level your book probably wouldn't have asked the question if there were not a good answer! :-)

Answer 3

Okay well 1 gallon equals 4.546 liters
So if you take the cube root of 4.546, you will get 1.65657007cm which would be the length of each side since it is a cube.

Answer 4

The last awnser looks right to me