A rectangular sheet 50 cm by 30 cm is rolled along the 30 cm side to form a cylinder (open at both ends). The radius of the cylinder is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 7.96 cm
When a sheet is rolled into a cylinder open at both ends, one side curls round to form the circumference of the circular ends and the other side becomes the height. The radius comes from the curled side: \(2\pi r=\) that side.
The answer given by NTA takes the 50 cm side as the circumference and the 30 cm side as the height:
The 50 cm side goes once round the circular end: \(2\pi r=50\)
Radius: \(\displaystyle r=\frac{50}{2\times3.1416}=\frac{50}{6.2832}\approx\) 7.96 cm
Note: The question says the sheet is rolled along the 30 cm side. In the usual meaning, the side along which a sheet is rolled becomes the circumference, which would give \(\displaystyle r=\frac{30}{2\pi}\approx4.77\) cm, and that value is not among the options. Only the other reading, with the 50 cm side curled round and the 30 cm side as the height, gives one of the options, so that is the reading used here. The question rolls the sheet one way, and NTA’s options roll it the other.