The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.
Since the diameter of the garden is 42m, the radius is half of that, which is:
r = 42m / 2 = 21m
The circumference of the circular garden is therefore:
C = 2πr = 2π(21m) = 42πm
If the gardener makes 4 rounds of the fence, he will need to purchase 4 times the circumference of the garden in barbed wire. Therefore, the length of barbed wire he needs to purchase is:
4 x 42πm = 168πm
This is approximately equal to 527.79m, if we use the value of π to two decimal places.