13. Five square tiles are put together side by side. A quarter circle is drawn on each tile to make a continuous curve as shown. Each of the smallest squares has side-length 1 .
What is the total length of the curve?
A $6 \pi$
B $6.5 \pi$
С $7 \pi$
D $7.5 \pi$
E $8 \pi$
Solution
A
The side lengths of the 5 squares are $1,1,2,3$ and 5 . So the curve is made up of five quarter circles with these radii. The circumference of a circle with radius $r$ is $2 \pi r$. Therefore the length of a quarter circle of radius $r$ is $\frac{1}{4}(2 \pi r)$, that is, $\frac{1}{2} \pi r$.

Therefore the length of the curve is $l$, where
$$
l=\frac{1}{2} \pi 1+\frac{1}{2} \pi 1+\frac{1}{2} \pi 2+\frac{1}{2} \pi 3+\frac{1}{2} \pi 5=\frac{1}{2} \pi(1+1+2+3+5)=6 \pi .
$$