17. The first figure shows four touching circles of radius $1 \mathrm{~cm}$ in a horizontal row, held together tightly by an outer band $\mathrm{X}$.
The second figure shows six touching circles of radius $1 \mathrm{~cm}$, again held tightly together by a surrounding band Y.
Which of the following statements is true?

A $\mathrm{X}$ is $2 \mathrm{~cm}$ longer than $\mathrm{Y}$
B $\mathrm{X}$ is $1 \mathrm{~cm}$ longer than $\mathrm{Y}$

C $\mathrm{X}$ and $\mathrm{Y}$ are the same length
$\mathrm{D} \mathrm{Y}$ is $1 \mathrm{~cm}$ longer than $\mathrm{X}$
$\mathrm{E} \mathrm{Y}$ is $2 \mathrm{~cm}$ longer than $\mathrm{X}$
17. C As shown in the upper figure, $X$ consists of two straight portions of length $6 \mathrm{~cm}$ and two semicircular arcs of radius $1 \mathrm{~cm}$.
So its length is $\left(2 \times 6+2 \times \frac{1}{2} \times 2 \pi \times 1\right) \mathrm{cm}=(12+2 \pi) \mathrm{cm}$.
In the lower figure, the band $\mathrm{Y}$ turns through one third of a revolution at each corner, so it consists of three straight portions of length $4 \mathrm{~cm}$ and three arcs, each of which is one third of the circumference of a circle of radius $1 \mathrm{~cm}$.
Hence its length is $\left(3 \times 4+3 \times \frac{1}{3} \times 2 \pi \times 1\right) \mathrm{cm}$ $=(12+2 \pi) \mathrm{cm}$.
So the two bands have the same length.