2. One side of a metal cube measures 2.69 inches. What is the volume of the cube in     cm³ ?

ANSWER: 3.20 x 10² cm³

SOLUTION

Given: 2.69 inches    Desired: cm³

As with any problem, there are several ways to solve this one. The obvious way is to convert 2.69 inches to cm and then cube the answer. Remember, cm x cm x cm = cm³. I will approach this problem differently.

We need to go from in³ to cm³. We are asked the volume of a cube. Each side of the cube measures 2.69 inches. We can use s³ to determine the volume of the cube in inches.

\(\displaystyle Volume\;=\;(2.69\;inches)^3\;=\;19.5\;in^3\)
 
Now, I need to convert in³ to cm³. Be careful. The equivalence, 1 in = 2.54 cm does not relate in³ to cm³–it relates cm and in. But, we can come up with an equivalence to relate in³ to cm³.

We know that 1 inch = 2.54 cm. That means (1 inch)³ = (2.54 cm)³. This simplifies to 1 in³ = 16.4 cm³. Now, we can write our conversion factors:

\(\displaystyle\require{cancel}\frac{16.4\;cm^3}{1\;in^3}\;or\;\frac{1\;in^3}{16.4\;cm^3}\)
 
Next, we set up our problem starting with our volume.

\(\displaystyle 19.5\;\cancel{in^3}\times\frac{16.4\;cm^3}{1\;\cancel{in^3}}\;=\;\mathbf{3.20\times{10^2}\;cm^3}\)
 
We could have simply converted the 2.69 inches to cm.

\(\displaystyle 2.69\;in\times\frac{2.54\;cm}{1\;in}\;=\;6.8\underline{3}26\;cm\)
Next,
 
\(\displaystyle (6.8\underline{3}26\;cm)^3\;=\;\mathbf{3.20\times{10^2}\;cm^3}\)
 
Go to Next Exercise
Back to Conversion Factors and Dimensional Analysis
Back to Study Guide List for General Chemistry 1