Question

A cylinder of circumference 8 cm and length 21 cm rolls without sliding for $4\frac{1}{2}$ seconds at the rate of 9 complete rounds per second.

Find:

(i) the distance travelled by the cylinder in $4\frac{1}{2}$ seconds, and

(ii) the area covered by the cylinder in $4\frac{1}{2}$ seconds.

Answer 1

Given: Circumference of the circle $=2\pi r=8cm$

$\therefore r=\frac{8\times 7}{2\times 22}=\frac{14}{11}cm$

Height of the cylinder $=21cm$

Therefore, CSA of the cylinder $=2\pi rh$

$=2\times \frac{22}{7}\times \frac{14}{11}\times 21$

$=168cm$

Now,

(i) No. rounds complete in $1$ second $=9$

$\therefore$ No. of rounds completed in $4\frac{1}{2}=4\frac{1}{2}\times 9$

Distance covered in $1$ round $=$ Circumference of the cylinder $=8cm$

Therefore, distance covered in $4\frac{1}{2}\times 9$ rounds$=4\frac{1}{2}\times 9\times 8=324cm$

(ii) Area covered in $1$ second $=9\times$ CSA of cylinder $=9\times 168$

$\therefore$ Area covered in $4\frac{1}{2}$ seconds $=9\times 168\times 4\frac{1}{2}=6804c{m}^2$