[問題]GWD3-Q8

chihkai1218

Q8:

A thin piece of wire 40 meters long is cut into two pieces.  One piece is used to form a circle with radius r, and the other is used to form a square.  No wire is left over.  Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?

 

A.      pr²

B.       pr² + 10

C.      pr² + ¼ p²r²

D.      pr² + (40-2pr)²

E.       pr² + (10- ½ pr)²

Answer: E

purplegosh

假设圆形为X

正方形为40-X

圆形周长X=2pr

正方形单边长=(40-X)/4,X可以带2pr

圆面积+正方形面积=pr²+(40-2pr/4)²

=pr²+(10-1/2pr)²