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).
2 Answers
hala718 | High School Teacher | (Level 1) Educator Emeritus
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