Perform this operation and report the answer to the correct number of significant figures: What is the mass of a cube of aluminum that is 4.0 cm on each edge? The density of aluminum is 2.7 g/cm3. Show all calculations leading to an answer.
volume = length * width * height
mass = volume * density
all of the given data is to two significant figures ... so the result should be also
To find the mass of the aluminum cube, we can use the formula: mass = density x volume.
First, let's find the volume of the cube. The volume of a cube is calculated by multiplying the length of one side by itself three times (since a cube has three dimensions).
Given that the cube has a side length of 4.0 cm, the volume can be calculated as:
volume = (4.0 cm)^3
volume = 4.0 cm x 4.0 cm x 4.0 cm
volume = 64.0 cm^3
Next, we can use the density of aluminum (2.7 g/cm^3) to find the mass of the cube.
mass = 2.7 g/cm^3 x 64.0 cm^3
mass = 172.8 g
Therefore, the mass of the aluminum cube is 172.8 grams.
Now, let's determine the number of significant figures to report the answer in. The given side length of the cube is given to 3 significant figures (4.0 cm). The density of aluminum is given to 2 significant figures (2.7 g/cm^3).
When multiplying or dividing values, the final result should be reported to the same number of significant figures as the value with the least number of significant figures. In this case, the density (2.7 g/cm^3) has the least number of significant figures.
Therefore, the mass of the aluminum cube should be reported to 2 significant figures:
mass = 170 g.