A drop of oil (volume 0.05cm3) is released from a medicine dropper on to the calm surface of a pond where it spreads out to cover an area of "40m2". Assume that the oil film has a uniform thickness equal to the diameter of a oil molecule.

Calculate the diameter of an oil molecule and express in Scientifc notation to an appropriate number of sig figs

volume = pi*r^2^thickness
volume = 0.05 cm^3
pi*r^2=area=40 cm^2
Calculate thickness.
Round to correct number of significant figures and change to scientific notation. Post your work if you get stuck.

I made a typo above on the first line.
It should be
volume = pi*r^2*thickness.
I believe everything else is ok.
Check my work.

To solve this problem, we can use the formulas provided and the given information.

The formula for the volume of a sphere is V = (4/3) * π * r^3, where V is the volume and r is the radius.

In this case, we are given the volume of the oil droplet as 0.05 cm^3. However, the volume formula we have is for a sphere, not a droplet. So we need to assume that the droplet is a sphere, which may not be entirely accurate in practical terms. Nevertheless, we will proceed with this assumption.

Since the volume of the sphere is given as 0.05 cm^3, we can rearrange the volume formula:

0.05 cm^3 = (4/3) * π * r^3

Next, we are given that the oil droplet spreads out to cover an area of 40 cm^2. The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius.

Therefore, we have the equation:

40 cm^2 = π * r^2

We can now rearrange this equation to solve for r:

r^2 = 40 cm^2 / π

Now we have two equations:

0.05 cm^3 = (4/3) * π * r^3

r^2 = 40 cm^2 / π

Let's solve the second equation for r:

r^2 = 40 cm^2 / π
r^2 ≈ 12.7324 cm^2

Now, since the thickness of the oil film is defined as the diameter of an oil molecule, we can assume the thickness is equal to 2 times the radius:

Thickness = 2 * r

Thickness = 2 * √(12.7324 cm^2)

Thickness ≈ 2 * 3.566 cm

Thickness ≈ 7.132 cm

Finally, to express the diameter of an oil molecule in scientific notation to an appropriate number of significant figures, we need to round the thickness value. The given significant figures are not mentioned, so we will assume 3 significant figures to keep the result meaningful and accurate:

Thickness ≈ 7.13 cm

Now, the diameter of an oil molecule is simply twice the thickness:

Diameter = 2 * Thickness

Diameter ≈ 2 * 7.13 cm

Diameter ≈ 14.26 cm

To express this result in scientific notation, we need to move the decimal point to the appropriate position. In this case, we need to move it two places to the left:

Diameter ≈ 0.1426 meters

Therefore, the diameter of an oil molecule, expressed in scientific notation to an appropriate number of significant figures, is approximately 1.43 x 10^-1 meters.