A drop of oil of volume 12^-10m^3 spreads out on water to make a circular film of radius 11^-2m calculate the thickness of the film
Thickness = volume / area
Area = πr² r = 11^-2
Area = 22/7 X 11^-2
Area = 0.02596m²
Volume = 12^-10m³
Thickness = 12^-10 / 0.02596
= 0.62211 * 10^-9
Or 6.22 * 10^-10
What if thickness is not given
To calculate the thickness of the film, we can use the formula for the volume of a cylinder.
The volume of the oil drop can be treated as a cylinder with a circular base, where the radius of the base is equal to the radius of the film. The volume of the oil drop is given as 12^-10m^3.
The volume of a cylinder is given by the formula:
V = πr^2h
Where V is the volume, r is the radius of the base, and h is the height (thickness) of the cylinder.
In this case, we have the volume (V = 12^-10m^3) and the radius (r = 11^-2m). We need to solve for the height (h).
First, rearrange the formula to solve for h:
h = V/(πr^2)
Now, substitute the given values into the equation:
h = 12^-10m^3 / (π * (11^-2m)^2)
Evaluate the expression:
h = 12^-10m^3 / (π * 11^-4m^2)
To simplify the expression, remember that (a/b)^-n is equivalent to (b/a)^n:
h = 12^-10m^3 / (π * 11^4m^2)
Next, multiply the numerator and denominator by 11^4m^2 to eliminate the negative exponent:
h = (12^-10m^3 * 11^4m^2) / (π * 11^4m^2)
Simplify the numerator:
h = (12^-10 * 11^4) / (π * 11^4m^2)
Now, calculate the value of the expression using a calculator:
h ≈ 0.003012 m
Therefore, the thickness of the film is approximately 0.003012 meters.
volume = area * thickness
so now just plug in your numbers