*This Math quiz is called 'Measurements - Cubic Inch and Cubic Feet' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.*

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You will have learned how to measure an area such as the area of a room. For example, if you wanted to buy a rug for a room, you would need to know how many square feet are in the room. To find the square footage you needed to multiply the length by the width so if a room was 14 feet long and 12 feet wide you multiplied 14 x 12 = 168. The rug you would need to purchase to fully cover the room’s floor would need to be 168 sq. ft.

Now what if you wanted to measure the air that was in that room? To measure air is to measure “**volume**”.

Volume refers to any object or thing (such as air or fluids) that it takes to fill up a 3-dimensional space such as a box. If you have a perfectly squared box this box would look like a cube. A cube is then measured in **cubic inches** or **cubic feet** depending upon the size of the area and the volume being measured. Cubic inches can be written as **cu. in.** or **in. ^{3}** and cubic feet can be written as

When measuring the surface of an area we had to multiply 2 surfaces to find the square footage of that area, i.e., length by width. When measuring the volume of an area we need to multiply three (3 dimensional) surfaces, i.e., length by width by height to find the volume. The formula to find the volume of an area is:

** Volume** = L x W x H

If you have box that is 12 feet long by 2 feet wide by 4 feet high then, you multiply the three measurements as follows:

12 x 2 x 4

12 x 2 = 24

24 x 4 = 96ft.^{3} (The volume of the box is 96 cubic feet or it can be written as 96 cu. ft.)

At times you will be required to find the cubic inch of an area. A cubic inch is the measurement of a cube that is 1in. x 1in. x 1in. = 1in.^{3}. If you were asked, “How many cubic inches are in a cubic foot?” well you know that there are 12 inches in 1 foot so this would give us 12in. x 12in. x 12in = 1,728in.^{3}.

Now how do you convert cubic inches to cubic feet? Let’s say you have 39in.^{3}. As there are 1,728in.^{3} in 1ft.^{3} (as we learned above) we need to divide 39in.^{3} by 1728 so: 39 ÷ 1728 = 0.0225694ft.^{3}. ** Solution:** 39in.

Understanding cubic measurement is important because there are many things in life that you will encounter that will be measured in a cubic measurement such as a refrigerator. If you are looking for a refrigerator, besides wanting to know how tall it is or how wide it is, you will want to know what the interior volume is because this is where you will be putting your food. If you look at refrigerators, they will always tell you the volume such as 22 cu. ft. or 25 cu. ft. Another area where you will run into cubic measurements is with tires, such as the tires on a car. Tires need to be inflated with air. Air is a measurement of volume so tires will need so many cubic inches or pounds of air pressure.

In many instances, such as pools, when you ask how much water is in the pool, you will be told that there are so many cubit feet of water or cubic yards of water rather than how many gallons of water are in the pool. In short, cubic measurement is a term you will see time and time again so learning and understanding where the measurement comes from will help you understand its usage in life. Many of you, depending upon the career you choose, will wind up using cubic measurements almost on a daily basis.

** NOTE:** One thing to note is to not confuse 5

Okay, let’s see if you understand the cubic inch and the cubic foot. Take a look at each of the following ten problems and see if you can locate the correct answer needed.

1.

Randy bought a new hot tub. It is 10 feet long by 8 feet wide by 3 feet deep. How many cubic feet of water will it take to fill up the hot tub?

260ft.^{3}

320ft.^{3}

280ft.^{3}

240ft.^{3}

2.

999in.^{3} = _____ft.^{3}

0.571825ft.^{3}

0.587125ft.^{3}

0.578125ft.^{3}

0.578215ft.^{3}

Working the problem you have:

1,728in.^{3} in 1ft.^{3} so we must divide 999in.^{3} by 1728

999 ÷ 1728 = 0.578125ft.^{3}

Answer (c) is the correct answer

1,728in.

999 ÷ 1728 = 0.578125ft.

Answer (c) is the correct answer

3.

27,420in.^{3} = _____ft.^{3}

15.688055ft.^{3}

15.868055ft.^{3}

15.860855ft.^{3}

15.868505ft.^{3}

Working the problem you have:

1,728in.^{3} in 1ft.^{3} so we must divide 27,420in.^{3} by 1728

27420 ÷ 1728 = 15.868055ft.^{3}

Answer (b) is the correct answer

1,728in.

27420 ÷ 1728 = 15.868055ft.

Answer (b) is the correct answer

4.

John and Janet want to buy a new oven. They want to make sure the oven will hold a 25lb. turkey so it must be at least 18 cu. ft., nothing smaller. The oven they are looking at has the measurement of 3 feet long by 3 feet wide by 2.5 feet high. Will this oven meet their 18 cu. ft. that they need?

22.5ft.^{3} (Yes it will be big enough)

17.5ft.^{3} (No it will not be big enough)

18.5ft.^{3} (No it will not be big enough)

21.5ft.^{3} (Yes it will be big enough)

Working the problem you have:

V = LWH

3 x 3 x 2.5

3 x 3 = 9

9 x 2.5 = 22.5

__Solution__: V = 22.5ft.^{3}

Yes, the oven will be big enough and Answer (a) is the correct answer

V = LWH

3 x 3 x 2.5

3 x 3 = 9

9 x 2.5 = 22.5

Yes, the oven will be big enough and Answer (a) is the correct answer

5.

411in.^{3} = _____ft.^{3}

0.2378472ft.^{3}

0.2378742ft.^{3}

0.2387472ft.^{3}

0.2738472ft.^{3}

Working the problem you have:

1,728in.^{3} in 1ft.^{3} so we must divide 411in.^{3} by 1728

411 ÷ 1728 = 0.2378472ft.^{3}

Answer (a) is the correct answer

1,728in.

411 ÷ 1728 = 0.2378472ft.

Answer (a) is the correct answer

6.

If you have boxcar that is 22 feet long by 5 feet wide by 8 feet high, what would be the cubic feet of the boxcar?

888ft.^{3}

808ft.^{3}

880ft.^{3}

800ft.^{3}

Working the problem you have:

V = LWH

22 x 5 x 8

22 x 5 = 110

110 x 8 = 880

__Solution__: V = 880ft.^{3}

Answer (c) is the correct answer

V = LWH

22 x 5 x 8

22 x 5 = 110

110 x 8 = 880

Answer (c) is the correct answer

7.

Martha was looking for a sandbox to put in the daycare’s playground. She needed the sandbox to hold at least 100 cubic feet of sand. The sandbox she was looking at was 7.5 feet long by 6.5 feet wide and was 1.5 feet deep. Will that sandbox hold the amount of sand that Martha wants it to hold?

103.25ft.^{3} (Yes it will be big enough)

83.25ft.^{3} (No it will not be big enough)

78.5ft.^{3} (No it will not be big enough)

73.125ft.^{3} (No it will not be big enough)

Working the problem you have:

V = LWH

7.5 x 6.5 x 1.5

7.5 x 6.5 = 48.75

48.75 x 1.5 = 73.125

__Solution__: V = 73.125ft.^{3}

No, the sandbox will not be big enough and Answer (d) is the correct answer

V = LWH

7.5 x 6.5 x 1.5

7.5 x 6.5 = 48.75

48.75 x 1.5 = 73.125

No, the sandbox will not be big enough and Answer (d) is the correct answer

8.

The new high school will have a skating rink in it. The rink will measure 72 feet long by 26 feet wide and the floor bed for the ice will be 2 feet deep. How many cubit feet of ice will the ice rink hold?

3,747ft.^{3}

3,447ft.^{3}

3,474ft.^{3}

3,744ft.^{3}

Working the problem you have:

V = LWH

72 x 26 x 2

72 x 26 = 1,872

1,872 x 2 = 3,744

Solution: V = 3,744ft.^{3}

Answer (d) is the correct answer

V = LWH

72 x 26 x 2

72 x 26 = 1,872

1,872 x 2 = 3,744

Solution: V = 3,744ft.

Answer (d) is the correct answer

9.

117in.^{3} = _____ft.^{3}

0.0677038ft.^{3}

0.0677083ft.^{3}

0.0678083ft.^{3}

0.0678038ft.^{3}

Working the problem you have:

1,728in.^{3} in 1ft.^{3} so we must divide 117in.^{3} by 1728

117 ÷ 1728 = 0.0677083ft.^{3}

Answer (b) is the correct answer

1,728in.

117 ÷ 1728 = 0.0677083ft.

Answer (b) is the correct answer

10.

A large, glass container was placed in the middle of the mall. It was filled with milk chocolate. The container was 6 feet long by 4 feet wide and 15 feet deep. How many cubic feet of milk chocolate was in the container?

325ft.^{3}

345ft.^{3}

360ft.^{3}

380ft.^{3}

Working the problem you have:

V = LWH

6 x 4 x 15

6 x 4 = 24

24 x 15 = 360

__Solution__: V = 360ft.^{3}

Answer (c) is the correct answer

V = LWH

6 x 4 x 15

6 x 4 = 24

24 x 15 = 360

Answer (c) is the correct answer

V = LWH

10 x 8 x 3

10 x 8 = 80

80 x 3 = 240

V = 240ft.Solution:^{3}Answer (d) is the correct answer