Question

Mike poured 15 cups of water into a rectangular container measuring 10 inches by 6 inches by 9 centimeters.

[1 cup = 14.44 cubic inches; 1 inch = 2.54 cm]

Part A: What is the maximum volume of water that the rectangular container can hold? Show your work. (3 points)

Part B: How many cubic inches of water was poured into the container? (3 points)

Part C: What was the height of the water in the container? Show your work. (4 points)

Measurement is given as length by width by height.

Answer 1

I've been told my handwriting is ugly so I'll try explaining unit cancellation one more time
\[\frac{ 1 inch }{ 2.54 cm }\]

if we want to convert 30 cm to inches we can just multiply and cancel the units out in our head\[30 cm * \frac{ 1 inch }{ 2.54 cm } = \frac{ 30 }{ 2.54 } = 11.811 inches\]

Answer 2

In part B we know 15 cups were poured in. Converting 15 cups into cubic inches using the formula they gave us,
[1 cup = 14.44 cubic inches]
\[15cups*\frac{ 14.44 inches^3 }{ 1 c up} = 15*14.44 cubic inches = 216.6 inches \]

Answer 3

@bibby where did you get 30cm

Answer 4

That was just a number I pulled out of nowhere for unit cancellation.

The way to approach THIS problem is
a) get them into one unit and multiply
b) copy whatever I just did

Answer 5

Part A:
V = L * W * H
V = 10" * 6" * 9 cm (convert 9cm to inches = 9 * 2.54 = 22.86)
V = 10 * 6 * 22.86
V = 1371.6
Now all measurement are in the same unit.

Part B:
1 cup is = 14.44 cubic inches

So, 14.44 * 15 = 216.6
216.6 cubic inches of water have been poured into the container.

Part C:
The maximum volume of water that the rectangular container can hold is V = 1371.6

Mike poured 216.6 cubic inches into the pan.

216.6 = 10 * 6 * H

216.6 / 60 = 3.61

Idk I think I forgot something ?

Answer 6

Think its my volume and height

Answer 7

high five brother you just embarrassed this old man excuse me while I take a seat and cry

Answer 8

Wacha mean :o

Answer 9

(convert 9cm to inches = 9 * 2.54 = 22.86)
This is incorrect

Answer 10

9/2.54 owned idiot nerd

Answer 11

Like it doesnt even make sense logically

Answer 12

Oh!! Knew something was wrong u.u

Answer 13

@bibby why would you divide 9/2.54??

Answer 14

To get the inches

Answer 15

2.54 cm in an inch

Answer 16

Yeah that's why I was spending time talking about cancelling the units in your mind. You have a ratio\[ \frac{ 1 inch }{ 2.54cm }\]

Answer 17

Its all abt proportions
1 inch : 2.54 cm
x inch: 9 cm

\(\large \frac{1}{x}=\frac{2.54}{9}\)

\( 9=2.54x\)

\(\large \frac{9}{2.54}=x\)

Answer 18

Ok my method is confusing -_-

Answer 19

Idk who is right here....

Answer 20

I'm using a chemistry method of unit cancellation lol

Answer 21

Im using what I learned in 8th grade lol

Answer 22

so fizic is wrong?

Answer 23

ok I'll just start from the beginning and outline what you're supposed to do at each step.

a: convert 9 cm into inches (divide by 2.54)
multiply that number, 10, and 6 to get the volume of the whole container.

B:
convert 15 cups into cubic inches by multiplying by 14.44
That is the amount poured into the container

Part C
We have all the dimensions but the height

[number from part b] = 10*6*x

Answer 24

Thank you~