SSC CPO SI and ASI 2011 Paper

(2)ΔABC is an equilateral with each side length equal to diameter.
ABHI, ADEC and BCFG are rectangles.
Also, ∠IAD = ∠FCE = ∠IAD = 360 – ∠IAB – ∠CAD – ∠BAC = 360 – 90 – 90 – 60 = 120 = ∠HBG = ∠FCE.
Now, length of the rubber band is,
$\mathit{H}\mathit{I}+\overline{\mathit{I}\mathit{D}}+\mathit{D}\mathit{E}+\overline{\mathit{E}\mathit{F}}+\mathit{F}\mathit{G}+\overline{\mathit{G}\mathit{H}}$
$=3\mathit{d}+3\times \frac{120}{360}\times 2\mathrm{\pi }\frac{\mathit{d}}{2}$
$=3\times 10+2\times \mathrm{\pi }\times \frac{10}{2}$
$=\left(30+10\mathrm{\pi }\right)\mathit{c}\mathit{m}$