The head of a nail is circular, as shown. The head of this nail has a diameter of 6 millimeters. Which millimeter is the closest to the area of the head of this nail in square centimeters?
The area of a circle is calculated using the formula A = πr^2, where r is the radius of the circle.
Since the diameter of the nail head is given to be 6 millimeters, the radius (r) is half of the diameter, so r = 6/2 = 3 mm.
Now, we can calculate the area of the nail head:
A = π*(3)^2
A ≈ 28.27 mm^2
To convert mm^2 to cm^2, we divide by 100 (since 1 cm^2 = 100 mm^2):
A ≈ 28.27 / 100
A ≈ 0.2827 cm^2
Therefore, the area of the head of this nail is closest to 0.283 cm^2.