if the diamter of a human hair is (50*10^-6 m) estimate the volume of hair on your head
To estimate the volume of hair on your head, we can make some assumptions:
1. The average thickness of human hair is about 50 micrometers (50 * 10^-6 meters).
2. The average number of hairs on a human head is approximately 100,000.
To estimate the volume, we can consider the hair as a cylindrical shape. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
1. First, let's calculate the radius of a single hair. The diameter given is 50 * 10^-6 meters, so the radius would be half of that which is 25 * 10^-6 meters (25 micrometers).
2. Next, we can estimate the total volume by multiplying the volume of a single hair by the average number of hairs on a human head.
V_total = V_single_hair * Number_of_hairs
V_single_hair = π * (25 * 10^-6)^2 * h
Assuming the height (h) of a hair is approximately 1 centimeter (0.01 meters), the volume of a single hair would be:
V_single_hair ≈ 3.14 * (25 * 10^-6)^2 * 0.01
V_single_hair ≈ 1.963 * 10^-11 cubic meters
Now, let's use the average number of hairs on a human head (100,000) to estimate the total volume:
V_total ≈ (1.963 * 10^-11) * 100,000
V_total ≈ 1.963 * 10^-6 cubic meters
Therefore, the estimated volume of hair on your head is approximately 1.963 * 10^-6 cubic meters.