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?
~$\pi r^{2}$~
~$\pi r^{2}+10$~
~$\pi r^{2}+\frac{1}{4}\pi ^{2}r^{2}$~
~$\pi r^{2}+\left ( 40-2\pi r \right )^{2}$~
~$\pi r^{2}+\left ( 10-\frac{1}{2}\pi r \right )^{2}$~
cut into two pieces 并不意味着平分线段
计算的时候少算了一步:在用总长度40-圆长度2Πr的时候得出的是正方形的周长,所以要除以4才是边长...
这道题就很扯,专门把答案弄的很复杂,其实就是4a=π r^2 所以 a=0.5 π r^2. 所以答案应该是 πr^2+ o.25π^2r^2;
把E选项化开,就是πr^2+100-10πr+o.25π^2r^2; 又因为2πr=20, 所以 πr=10, 所以 πr^2+100-10πr+o.25π^2r^2= πr^2+ o.25π^2r^2
这两个线段是不等长的,所以答案其实有道理的
登录 或 注册 后可以参加讨论