SOLUTION: Find the area of the band between two concentric circles if their diameters are 10 centimeters and 6 centimeters.

Algebra ->  Circles -> SOLUTION: Find the area of the band between two concentric circles if their diameters are 10 centimeters and 6 centimeters.      Log On


   

Question 1071502: Find the area of the band between two concentric circles if their diameters are 10 centimeters and 6 centimeters.
Found 2 solutions by Boreal, math_helper:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Area of larger is pi*25, since 10 cm has a radius of 5 cm.
Area of smaller is pi*9
The area between them is (25 pi-9 pi)=16 pi cm^2 or 50.27 cm ^2.

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is solved by noting that the area of a circle is %28pi%29+r%5E2 and using that to calculate the area of the larger circle and the smaller circle. The smaller circle's area is then subtracted from the larger, as we're interested in the band, or "washer," between them:
---
The area of the outer circle is +A_outer+=+%28pi%29%2810%2F2%29%5E2+
The area of the inner circle is +A_inner+=+%28pi%29%286%2F2%29%5E2+
The area of the band is A_outer-A_inner = +%28pi%29%2810%2F2%29%5E2+-+%28pi%29%286%2F2%29%5E2+
= +%28pi%29%285%5E2%29+-+%28pi%29%283%5E2%29+
= +%28pi%29%2825%29+-+%28pi%29%289%29+
= +highlight%2816%28pi%29+cm%5E2%29+ or around +highlight%2850.27%29+ +cm%5E2+