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

• A. $6104$ $c{m}^2$ Area covered by the cylinder in 1 round $=$ its curved surface area.
• B. $6804$ $c{m}^2$ Area covered by the cylinder in 1 round $=$ its curved surface area.
• C. $6404$ $c{m}^2$ Area covered by the cylinder in 1 round $=$ its curved surface area.
• D. $6204$ $c{m}^2$ Area covered by the cylinder in 1 round $=$ its curved surface area.

Answer 1

The correct option is B $6804$ $c{m}^2$ Area covered by the cylinder in 1 round $=$ its curved surface area.

Given , A cylinder with circumference 8 cm and length 21 cm.
Number of round per second$=$ 9
Number of round in $4\frac{1}{2}$ seconds $=4\frac{1}{2}\times 9$
$=\frac{81}{2}$
Circumference of cylinder$=$ 8 cm
or, $2\pi r$ $=$ 8 cm
or, $r$ $=\frac{8}{2\pi }$
Curved surface area of cylinder= $2\pi rh$
= $2\times \frac{22}{7}\times \frac{8}{2\pi }\times 21$
$=168{cm}^2$
Area covered in 1 round = Curved surface area
Area covered in $\frac{81}{2}$ rounds $=\frac{81}{2}\times$ curved surface area
$=\frac{81}{2}\times 168$
$=6804{cm}^2$