A circular path two feet wide has an inner diameter of 150 feet. How much farther is it around the outer edge of the path than around the inner edge ?
remember ,
circumference = dπ, where d is the diameter
so what is the diameter of the outer part of the path?
12.56
To find out how much farther it is around the outer edge of the path than around the inner edge, we need to calculate the circumference of each circle and then find the difference between the two.
First, let's calculate the circumference of the inner circle. The circumference of a circle can be found using the formula C = πd, where C is the circumference and d is the diameter. In this case, the diameter of the inner circle is given as 150 feet.
Circumference of inner circle = π * 150 = 150π feet
Now, let's calculate the circumference of the outer circle. The outer diameter will be the sum of the inner diameter and the width of the path. In this case, the width of the path is given as 2 feet.
Outer diameter = inner diameter + 2 * width of the path
= 150 + 2 * 2
= 150 + 4
= 154 feet
Circumference of outer circle = π * 154 = 154π feet
To find the difference in circumference, we subtract the circumference of the inner circle from the circumference of the outer circle.
Difference in circumference = Circumference of outer circle - Circumference of inner circle
= 154π - 150π
= 4π feet
Therefore, the path around the outer edge is 4π feet farther than around the inner edge.