Question

Can someone please help me with this?

Dan poured 5 cups of water into a rectangular container measuring 8 inches by 6 inches by 7 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

How do you find the volume of a rectangular solid?

Answer 2

\(V = LWH\)

Answer 3

For part A, use the dimensions of the rectangular solid and the volume formula above and find its volume.

Answer 4

@mathstudent55 But how do you convert the centimeters for part A?

Answer 5

Divide inches by 2.54 to get cm.

Answer 6

So you divide 7 by 2.54 and get 2.76?

Answer 7

Notice that the cm units cancel out leaving in.

Answer 8

Ok. So the final answer for part a is 132.28 cubic inches?

Answer 9

Correct. That is the answer for part A.

Answer 10

How do I do part B?

Answer 11

\( V = LWH\)

\(V = 8~in. \times 6~in. \times 7~cm \times \dfrac{1~in.}{2.54~cm} = 132.28 in.^3\)

Answer 12

Now part B.
How much water was poured into the container?

Answer 13

5 cups

Answer 14

Right. Now we need to convert 5 cups into cubic inches.

Answer 15

We are told that 1 cup = 14.44 cubic inches.

Answer 16

\(5~cups \times \dfrac{14.44~in.^3}{1~cup} =\)

In this case, we multiply the amount in cups by 14.44 to get cubic inches.

Answer 17

So the answer is 72.2 cubic inches for part B?

Answer 18

Correct.

Answer 19

Ok. What about the last part?

Answer 20

Now part C.
Remember the formula for the volume of a rectangular solid:

\(V = LWH\)

For this part of the problem, we know the volume, the length and the width. We need the height of the water.

Answer 21

We substitute the known quantities in the volume formula and solve for H.

\(V = LWH\)

\(72.20 ~in.^3 = 8~in. \times 6~in. \times H\)

Answer 22

\(72.20~in.^3 = 48~in.^2 \times H \)

To find H, we divide both sides of the equation by 48 in^2.

Answer 23

So the answer is 1.50 cubic inches?

Answer 24

Correct.
Good job!

Answer 25

But then what was the 132.28 cubic inches?

Answer 26

@mathstudent55

Answer 27

Sorry. You got the number right, but not the units.
The last answer is simply 1.50 inches, not 1.50 cubic inches.
Part C. is asking for the height of the water in the container.
When solving the equation, you have 72.20 in^3 on the left side.
When you divide that by 48 in^2, you get 1.50 in.
in.^3 divided by in.^2 = in.