Tracey has two empty cube-shaped containers with sides of 5 inches and 7 inches. She fills the smaller container completely with water, and then pours all the water from the smaller container into the larger container. How deep, to the nearest tenth of an inch, will the water be in the larger container?
Please tell me how you did it. If possibe, show work.
THANKS! :)
2007-12-28 06:02:07 · 13 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
She is filling the second container with 125 inches cubed of water, now you have to divide that by 7*7=49 to get the height of the space it's going to fill which is 2.6 inches.
(125 inches cubed)/(49 inches squared) = 2.6 inches
2007-12-28 06:40:26 · answer #1 · answered by Anonymous · 0⤊ 1⤋
OK. Let's start with the smaller container:
Volume = length x width x height
If we're talking about a cube 5 * 5 * 5, the volume is 125 cubic inches.
Now let's apply that to the other container. We know if we pour all the water into the container it will still be 125 cubic inches of water, and we also know that the base of the other cube is 7 * 7. What we don't know is the height. So let's make a formula out of it:
125 = 7 * 7 * x
Multiply the one side out and you get:
125 = 49x
Divide both sides by 49 and you get:
x = 125/49, and if you use a calculator you get 2.55102, so the depth in the larger container (to the nearest 1/10 of an inch) would be 2.6 inches.
2007-12-28 14:09:33 · answer #2 · answered by Anonymous · 2⤊ 0⤋
One cube has 5 inch sides, so its 5 X 5 X 5 giving it 125 cubic inches of water. The other has 7 inch sides, so its 7 X 7 X 7 giving it 343 cubic inches of space.
Every inch of water in small cube is 5 x 5 or 25 square inches
Every inch of space in large cube is 7 x 7 or 49 square inches
so you take the volume of the small cube, 125, and divide it by the ammount it will take to fill 1 inch of the larger cube.
125/49 = 2.55
That is how deep the water will be in the large cube. 2.6 inches.
2007-12-28 14:14:54 · answer #3 · answered by Puzzled 2 · 0⤊ 0⤋
1st step find the volume of the water involved. That is, the volume of the smaller cube-shaped containers. Using a simple cube equation by finding the cube of the length.
5^3 = 125inch squares.
2nd step. That's the amount of water involved. Once Tracey poured it into the bigger cube shaped container, it no longer takes the shape of a cube. It's now a rectangular prism with a square of 7x7 inches for a base. Put this into equation for volume of a block.
volume = height x area of base
=height x 7^2
now the volume = 125 inch squares remember?
so
125 = height x 49
height = 125/49
2007-12-28 14:10:28 · answer #4 · answered by Anonymous · 1⤊ 0⤋
volume of smaller container = 5 x 5 x 5 = 125 inch square
volume of larger container = base area x height
125 = (7 x 7) x height
height = 125 / 49
= 2.6 inch (correct to nearest tenth)
2007-12-28 14:07:55 · answer #5 · answered by Lightofwadowice 5 · 3⤊ 0⤋
Find the volume of each cube. Divide the smaller by the larger to find the percentage. That is the percentage of water in the smaller cube compared to the volume of the larger cube. Multiply the percentage by 7 inches.
2007-12-28 14:17:49 · answer #6 · answered by JLuna 1 · 0⤊ 1⤋
5 inch cube holds 5 x 5 x 5 or 125 cubic inches
7 in cube holds 7 x 7 x 1 or 49 cubic inches per inch of depth
Therefore 125 / 49 = 2.55
49 times 2.55 = 124.95 cubic inches
2007-12-28 14:10:26 · answer #7 · answered by Contented 6 · 1⤊ 0⤋
volume of small container = s^3 = 5^3 = 125 in^3
volume of larger container = 7^3 = 343 in^3
So 49h = 125
h = 2.6 inches = height of water in 7" cube
2007-12-28 14:10:43 · answer #8 · answered by ironduke8159 7 · 4⤊ 0⤋
V (water) = 125 in ³
7 x 7 x h = 125
h = 125 / 49 in
h = 2.6 in
2007-12-28 15:04:31 · answer #9 · answered by Como 7 · 3⤊ 0⤋
125 = 5*5*5 cu. in of water in the 7 inch
7*7 49 sq. in. height of base
125/49 in of water approx. 2.6 in.
2007-12-28 14:08:25 · answer #10 · answered by digit 1 · 3⤊ 0⤋