Question

A cylinder of circumference$8$cm and length$21$cm rolls without sliding
for$4\dfrac{1}{2}$seconds at the rate of$9$complete rounds per second. Find the area covered
by the cylinder in$4\dfrac{1}{2}$ seconds.
A. $6104c{m^2}$Area covered by the cylinder in $1$round$ = $its curved surface area.
B. $6804c{m^2}$Area covered by the cylinder in $1$round$ = $its curved surface area.
C. $6404c{m^2}$Area covered by the cylinder in $1$round$ = $its curved surface area.
D. $6204c{m^2}$Area covered by the cylinder in $1$round$ = $its curved surface area.

Answer 1

Hint: Find the curved surface area of the cylinder using the formula:
Curved surface area$ = \left( {{\text{Circumference of cylinder}}} \right)\left( {{\text{Length
of cylinder}}} \right)$
Use the curved surface area to find the area covered in one second and then use it to find the area
covered in $4\dfrac{1}{2}$ seconds.
We have given that there is a cylinder of circumference$8$cm and length$21$cm that rolls
without sliding for$4\dfrac{1}{2}$seconds at the rate of$9$complete rounds per second.
We have to find the area covered by the cylinder in$4\dfrac{1}{2}$seconds.
Given
Circumference of cylinder$ = 8$cm
Length of cylinder$ = 21$cm
Find the curved surface area of the cylinder using the formula:
Curved surface area$ = \left( {{\text{Circumference of cylinder}}} \right)\left( {{\text{Length
of cylinder}}} \right)$
Substitute the values of the circumference and the length of the cylinder into the equation:
Curved surface area$ = \left( 8 \right)\left( {21} \right)$
Curved surface area$ = 168{\text{ c}}{{\text{m}}^2}$
So, the area covered by the cylinder in one complete round is $168{\text{ c}}{{\text{m}}^2}$
and we have to find the area covered by the cylinder in 9 complete rounds.
The area covered by the cylinder in 9 complete rounds is given as:

Area covered in 9 complete rounds$ = 9\left( {{\text{Area covered in one complete round}}}
\right)$
Area covered in 9 complete rounds$ = 9\left( {168} \right)$
Area covered in 9 complete rounds$ = 1512{\text{ c}}{{\text{m}}^2}$.
So, the area covered by the cylinder in one second is $1512{\text{ c}}{{\text{m}}^2}$. Now
find the area covered by the cylinder in $4\dfrac{1}{2} = \dfrac{9}{2}$seconds.
So, the area covered by the cylinder is $4\dfrac{1}{2} = \dfrac{9}{2}$seconds is given as:
Area covered$ = \dfrac{9}{2}\left( {{\text{Area covered in one second}}} \right)$
Substitute the value of the area covered in one second into the equation:
Area covered$ = \dfrac{9}{2}\left( {1512} \right)$
Area covered$ = 6804{\text{ c}}{{\text{m}}^2}$

So, the area covered by the cylinder in $4\dfrac{1}{2} = \dfrac{9}{2}$seconds is $ =
6804{\text{ c}}{{\text{m}}^2}$.
So,option B is the correct answer
Note: If a cylinder is rolling without sliding, then the area covered by the cylinder is equal to the
curved surface area of the cylinder.