A box has a volume of 592 cm³. What is the volume in inches cubed if one inch is equal to 2.54 cm?

Question

Quizplus · Accepted Answer

In order to convert between different units of measurement, we use what is called a conversion factor. A conversion factor is a ratio (written as a fraction) where one of the units is the numerator and one is the denominator. In order to convert one type of unit to another, you will cross-multiply the starting value by the conversion factor. *We decide which unit goes on the top based on what we are trying to convert. Basically, the units have to match - the units of one numerator should be the same as the numerator of the second fraction. In this case, we know the conversion factor to be the number of centimeters in one inch. This can be written as either of the following: ^{2.54 cm} / _{1 in} OR ^{1 in} / _{2.54 cm} These can both be used as conversion factors because the ratio of inches to centimeters is the SAME in both. In order to decide which version to use, we come to our problem. We are told that we have 592 cm³, and we're trying to convert the centimeters to inches. Since the number of inches is unknown, we're going to represent it as x. In order to solve using ratios, we need to write the first ratio as a fraction. We know that we have 592 cm³, so that will be the numerator in our fraction (ratio) to start. We have decided to use x to represent the unknown number of inches, so our fraction (ratio) will look like this: ^{592 cm3}/_x Now, we know which version of the conversion factor to use. Centimeters is the unit used in the numerator, so we will use the conversion factor that also has centimeters in the numerator: ^{2.54 cm}/_{1 in} Now we can set the ratios equal to one another in preparation to solve. ^{592 cm3}/_x= ^{2.54 cm}/_{1 in} However, before we can move forward, we have to make sure the units match. Even though we're using inches and centimeters in each, the left hand side of the equation has cubed units, while the right hand side does not. We cannot combine terms if they don't have the same units. Remember that when something is "cubed," it means that it has been multiplied by itself, twice. For example: 2³= 2 • 2 • 2 = 8 3²= 3 • 3 • 3 = 27 2 meters • 2 meters • 2 meters = 8m³ Therefore, in order to "cube" the right side of the equation, we are going to multiply the entire ratio (fraction) by itself, twice (and round any decimals to the nearest tenth to make the math easier!) ^{2.54 cm}/_{1 in}• ^{2.54 cm}/_{1 in} • ^{2.54 cm}/_{1 in} = ^{16.39 cm3}/_in³ Now, we can move forward and solve. ^{592 cm3}/ _x= ^{16.39 cm3}/ _in³ Cross multiply across the equal sign to eliminate the ratios. This means you multiply the first numerator by the second denominator, and the first denominator by the second numerator. 592 cm³ • 1 in³ = x • 16.39 cm³ 592 cm³ • in³ = x • 16.39 cm³ Now, we can see that we have the 16.39 cm³ multiplying the x, so we have to divide both sides by 16.39 cm³. Note that when you divide, you also divide by the units. This cancels out the cm on the left hand side as well. 592 cm³ • in³ ÷ 16.39 cm³= x • 16.39 cm³÷ 16.39 cm³ 36.12 in³ = x Since the answers are given as whole numbers, we just need to round our answer to the nearest whole number. 36.12 → 36

A Box Has a Volume of 592 Cm3

A Box Has a Volume of 592 Cm³