GATE 2024 EC – Question 7
Four identical cylindrical chalk-sticks, each of radius $r=0.5$ cm and length $l=10$ cm, are bound tightly together using a duct tape as shown in the following figure.
The width of the duct tape is equal to the length of the chalk-stick. The area (in cm$^2$) of the duct tape required to wrap the bundle of chalk-sticks once, is
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Correct answer: (D) $10\,(4+\pi)$
Explanation
The four sticks are packed in a $2\times2$ square arrangement. A tape wrapped tightly around them follows four straight sections of length $2r=1$ cm (between neighbouring circles) and four quarter-circle arcs that together make a full circle of radius $r$, of length $2\pi r=\pi$ cm. The perimeter of the cross-section is $4+\pi$ cm. The tape is 10 cm wide, so its area is $10(4+\pi)$ cm$^2$.