Question

A roller of diameter $70\text{ }cm$ and length \[2\text{ }m\] is rolling on the ground. What is the area covered by the roller in \[50\] revolutions?
A $220\text{ }{{m}^{2}}$
B $230\text{ }{{m}^{2}}$
C $210\text{ }{{m}^{2}}$
D $330\text{ }{{m}^{2}}$

Answer 1

Hint: Here we use the concept of 3D Figures.
Required Formula:
$Surface\text{ }Are{{a}_{cylinder}}=2\pi rh$
Given: Diameter of roller \[=70cm\Rightarrow r=35\text{ }cm=0.35\text{ }m\]
Length of roller is \[2\text{ }m\]

Complete step-by-step answer:
 Let $r$ be the radius of the base of the roller.
Let $h$ be the length of the roller.
According to the question, the height of the roller becomes the length of the roller.
Area covered by the roller in \[50\] revolutions is:
 $50\times Surface\text{ }Area\text{ }of\text{ }the\text{ }roller$
$\begin{align}
  & =50\times 2\times \pi \times r\times h \\
 & =50\times 2\times \dfrac{22}{7}\times 0.35\times 2 \\
 & =220\text{ }{{m}^{2}} \\
\end{align}$
Therefore, area cover by roller in \[50\] revolutions is $220\text{ }{{m}^{2}}$ .
Hence Option choice A is the correct answer.

Note: In such type of questions which involves concept of3D Figures having knowledge about the formula and the meaning of the terms is needed. Frame the equations accordingly to get the required value.