Question

The curved surface of a cylinder is developed into a square whose diagonal is 2√2 cm. The area of the base of the cylinder (in cm²) is

(a) 3π 

(b) \(\frac1π\)

(c) π 

(d) 6π

Answer 1

(b) \(\frac1π\) cm²

Each edge of the square = \(\frac{1}{\sqrt2}\times2\sqrt2=2\) cm 

If ‘r’ is the radius of the cylinder, then circumference of base of cylinder = edge of square

⇒ 2πr = 2 ⇒ r = \(\frac1π\)

∴ Area of base = πr² = π x \(\big(\frac1π\big)^2=\frac1π\) cm².