SOLUTION: Find the percentage areas for: ( correct 1 decimal place) a) the largest square inside a circle b) the largest circle inside a square Please show all working. Thankyou

Algebra ->  Surface-area -> SOLUTION: Find the percentage areas for: ( correct 1 decimal place) a) the largest square inside a circle b) the largest circle inside a square Please show all working. Thankyou      Log On


   

Question 1018930: Find the percentage areas for: ( correct 1 decimal place)
a) the largest square inside a circle
b) the largest circle inside a square
Please show all working. Thankyou
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a) If the square is inside the circle, the diameter(D%5Bc%5D) of the circle is equal to the diagonal of the square, D%5Bs%5D.
A%5Bs%5D=s%5E2
So then,
D%5Bs%5D%5E2=s%5E2%2Bs%5E2=2s%5E2
and
A%5Bc%5D=%28pi%2F4%29%2AD%5Bc%5D%5E2
A%5Bc%5D=%28pi%2F4%29%2A%282s%5E2%29
A%5Bc%5D=%28pi%2F2%29s%5E2
So then,
A%5Bs%5D%2FA%5Bc%5D=%28s%5E2%29%2F%28%28pi%2F2%29%2As%5E2%29
A%5Bs%5D%2FA%5Bc%5D=2%2Fpi
b) If the circle is inside the square then the diameter of the circle will equal a side of the square.
A%5Bs%5D=s%5E2
A%5Bc%5D=%28pi%2F4%29D%5Bc%5D%5E2=%28pi%2F4%29s%5E2
So then,
A%5Bc%5D%2FA%5Bs%5D=%28%28pi%2F4%29s%5E2%29%2Fs%5E2
A%5Bc%5D%2FA%5Bs%5D=pi%2F4