SOLUTION: I have this problem: The area of a rectangle is (25)(pi^2) cm^2. What is the diameter of a circle that has the same area as the area of the rectangle? My answer was 10pi. The textb

Algebra ->  Surface-area -> SOLUTION: I have this problem: The area of a rectangle is (25)(pi^2) cm^2. What is the diameter of a circle that has the same area as the area of the rectangle? My answer was 10pi. The textb      Log On


   

Question 1104854: I have this problem: The area of a rectangle is (25)(pi^2) cm^2. What is the diameter of a circle that has the same area as the area of the rectangle? My answer was 10pi. The textbook's answer was 10sqrtpi. What did I do wrong? Thanks for your time!
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Area for both the rectangle and the circle: 25pi%5E2

The circle, area using radius r:
pi%2Ar%5E2=25pi%5E2
r%5E2=25pi%5E2%2Fpi
r%5E2=25pi
r=5%2Asqrt%28pi%29

The diameter of the circle is twice r.
highlight%28d=2r=10%2Asqrt%28pi%29%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
S%5Bcircle%5D = pi%2Ar%5E2 = 25%2Api%5E2  ====>


r%5E2 = 25%2Api    ====>    r = sqrt%2825%2Api%29 = 5%2Asqrt%28pi%29    ====>  D= diameter = 2r = 10%2Asqrt%28pi%29.