A round barn with 75 m circumference is surrounded by a fence that is 10 m from the barn all around. How long is the fence?I don't understand how to get the radius of the origional circle (the barn).
We will use the circumference formula to find the original radius.
We know that:
C = 2*r*pi where r is the radius.
Given that the circumference is 75 m.
==> 75 = 2*r*pi
Now we will divide by 2pi.
==> r= 75/2pi = 11.94 m (approx.)
Now we know that the distance between the circle and the fence is 10 m.
Then the radius of the circular fence is r+ 10 = 11.94+10 = 21.94 m.
Now we will calculate the circumference of the fence given the radius 21.94.
==> C = 2*pi * r = 2*pi * 21.94 = 137.83 m
Then the length of the fence is 137.83 m
The circular barn has a circumference of 75 m. For a circle of radius r, the circumference is given as 2*pi*r
2*pi*r = 75 m
=> r = 75/2*pi
The fence has been constructed all around the barn at a distance of 10 m from it. This gives the radius of the circle formed by the fence as 10 + 75/2*pi
The length of the fence is 2*pi*(10 + 75/2*pi)
=> 20*pi + 75
The required length of the field is 20*pi + 75 or 137.83 m