A cylinder of circumference 8 cm and length 21 cm rolls without sliding for 4½ seconds at the rate of 9 complete rounds per second. Find: (i) distance travelled by the cylinder in 4½ seconds, and (ii) the area covered by the cylinder in 4½ seconds
A cylinder of circumference 8 cm and length 21 cm rolls without sliding for 4½ seconds at the rate of 9 complete rounds per second. Find: (i) distance travelled by the cylinder in 4½ seconds, and (ii) the area covered by the cylinder in 4½ seconds

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(A) - 1

Base circumference of cylinder (c) = 8 cm

So, the radius

    \[=\text{ }c/2\pi \text{ }=\text{ }\left( 8\text{ x }7 \right)/\text{ }\left( 2\text{ x }22 \right)\text{ }=\text{ }14/11\text{ }cm\]

Length of the cylinder (h) = 21 cm

(i) If distance covered in one revolution is 8 cm, then distance covered in 9 revolutions = 9 x 8 = 72 cm or distance covered in 1 second = 72 cm.

Thus, distance covered in 4½ seconds

    \[=\text{ }72\text{ x }\left( 9/2 \right)\text{ }=\text{ }324\text{ }cm\]

(ii) Curved surface area

    \[\begin{array}{*{35}{l}} =\text{ }2\pi rh  \\ =\text{ }2\text{ x }22/7\text{ x }14/11\text{ x }21  \\ =\text{ }168\text{ }c{{m}^{2}}  \\ \end{array}\]

So, the area covered in one revolution = 168 cm2

Then,

The area covered in 9 revolutions

    \[=\text{ }168\text{ x }9\text{ }=\text{ }1512\text{ }c{{m}^{2}}\]

Which is also the area covered in 1 second = 1512 cm2

Therefore, the area covered in 4½ seconds

    \[=\text{ }1512\text{ x }9/2\text{ }=\text{ }6804\text{ }c{{m}^{2}}\]