Question

A square sheet with side 2π cm is rolled into a cylinder along one of its sides. What is the volume of the cylinder?

• A. 4${\pi }^2$ cm${}^3$
• B. 8${\pi }^3$ cm${}^3$
• C. 2${\pi }^2$ cm${}^3$
• D. 2${\pi }^4$ cm${}^3$

Answer 1

The correct option is C 2${\pi }^2$ cm${}^3$


Given,
Side of square = 2π cm
⇒ height of cylinder = 2π cm

The side of the square is the circumference of the circular base of the cylinder. Let the radius of the cylinder be "r".

Hence,
2πr = 2π
r = 1 cm

So, the volume of the cylinder is,
$\pi r^{2}h=2{\pi }^2$ cm${}^3$