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

I'll do everything in inches

(10 cm = 3.937 in)

So A is

10 * 6 * 3.937 = 236.22 cu. in.

B is

15 * 14.44 = 216.6 cu. in.

C is

(volume of water = ht. of water * area of the base).......  therefore.......

(volume of water/ area of the base = ht. of water)

216.6 cu. in / 60 sq. in =

3.61 inches

Part A:

It doesn't say whether we want the maximum volume in cubic inches or cubic centimeters, but we have to convert the dimensions (height, width, length) into the same base to get an answer. Let's convert all the dimensions to centrimeters, because it seems the easiest. You can then turn it back into inches if you need to.

The dimensions are 10 inches by 6 inches by 10 centimeters.

2.54 cm in an inch, so 10*2.54 and 6*2.54 tells us these measurements in cm.

10*2.54 = 25.4

6*2.54 = 15.24

Our new dimensions are 25.4 cm by 15.24 cm by 10 cm

To get the volume, multiply length times height times width.

$$25.4\;cm\times15.24 \;cm\times 10 \;cm = 3870.96\; cubic \;cm$$

So our answer is 3870.96 cubic cm.

Part B:

We are also told 1 cup = 14.44 cubic inches.

Mike poured 15 cups into the container.

15*14.44

216.6 cubic inches

Part C:

Disclaimer: I'm not quite sure if this is how you do this part...but I'm pretty sure this is right.

We know that 216.6 cubic inches is how much water there is in the container. Let's turn this to cubic cm.

216.6*2.54 = 550.164 cubic cm.

Our dimensions in cm are 25.4 cm by 15.24 cm by 10 cm.

Now just divide this by length and width and we'll get how high the water went up to in this container.

550.164 ÷ 25.4 ÷ 15.24 = 1.421259842519685

Or, rounded to the nearest hundredth, 1.42 cm.

I haven't looked very hard but these answers do not appear the same  

1.42cm is not equal to 3.61inches