Question

A sheet of aluminum foil that has a thickness of 0.100 micrometers has dimensions of 24.0 cm x 15.0 cm. How many milligrams would this sample weigh if the density of aluminum is 2.70 g/cm^3

Answer 1

The mass will be $9.72*10^{-3}g$.

The volume of a rectangular solid or sheet is equal to its length (l) times width (w) times thickness (t) or height.

Given:

Thickness (h)= 0.100 micrometers

1 centimeter = 10,000 micrometer

1 micrometer= 1/10,000 centimeter

0.100 micrometer= 0.100/10,000 centimeter

• Thickness= $1*10^{-5}cm$
• Length= 24.0 cm
• Width= 15.0 cm
• Density= $2.70 g/cm^3$

Lets, calculate volume first.

$\text{Volume}=l*b*h\\\\\text{Volume}= 24*15*10^{-5}\\\\\text{Volume}=360*10^{-5}\\\\\text{Volume}=3.6*10^{-3}cm^3$

Density:

It is defined as the ratio of mass over volume.

$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$

On substituting the values in the above formula:

$\text{Density }=\frac{\text{Mass}}{\text{Volume}}\\\\\text{Mass}=\text{Density}*\text{Volume}\\\\\text{Mass}=2.70*3.6*10^{-3}\\\\\text{Mass}=9.72*10^{-3} g$

Thus, the mass will be $9.72*10^{-3}g$.

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