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 cu. ft. or ft.3.
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 or V = LWH
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.3 = 0.0225694ft.3.
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 53 with 5ft.3. The first number is just that – a number to the third power or a number that is multiplied by itself three times, i.e., 5 x 5 x 5. The second number is the measurement of volume. It was derived by measuring length by width by height. It is not 5 ft. x 5 ft. x 5 ft.
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.