Question

A rectangular piece of paper is 24 cm long and 22 cm wide. A cylinder is formed by rolling the paper along its length. The volume of the cylinder is 

(a) 924 cm³ 

(b) 462 cm³ 

(c) 264 cm³ 

(d) 528 cm³ 

Answer 1

(a) 924 cm³

Let the radius of the cylinder be R. 

Since the cylinder is formed by rolling the rectangular sheet along its length, circumference of base of cylinder = 2πR = width of the sheet, 

i.e.,

2 x \(\frac{22}{7}\) x R = 22 cm

⇒ R = \(\frac72\) cm.

Height of cylinder = length = 24 cm 

∴ Volume of the cylinder = πR²h

= \(\frac{22}{7}\times\frac72\times\frac72\times24\) cm³ = 924 cm³.