Question

A cylinder of circumference 8 cm and length 21 cm rolls without sliding for `4 1/2` seconds at the rate of 9 complete rounds per second. Find the area covered by the cylinder in `4 1/2` seconds.

Answer 1

Circumference of cylinder = 8 cm

Therefore, radius = `c/(2pi) = (8 xx 7)/(2 xx 22) = 14/11 cm`

Length of the cylinder (h) = 21 cm 

Curverd surface area = 2πrh 

= `2 xx 22/7 xx 14/11 xx 21`

= 168 cm²

Area covered in one revolution = 168 cm²

Area covered in 9 revolution = 168 cm² × 9 = 1512 cm²

Therefore, area covered in 1 second = 1512 cm²

Hence, area covered in `4 1/2` seconds = `1512  cm^2 xx 9/2`

= 6804 cm²