question_answer

A cylinderical road roller has its length two times its base radius. If the base radius is 42 cm. How much area does it level, if it rolls once?

A) \[22176\,\,c{{m}^{2}}\]           

B) \[22374\,\,c{{m}^{2}}\]

C) \[21220\,\,c{{m}^{2}}\]                       

D) \[25370\,\,c{{m}^{2}}\]

Correct Answer: A

Solution :

Here, r = 42 cm and length of the roller (h) \[=2r\]

Length of the roller \[=2\times 42=84\,\,cm\]

When the roller rolls cover an area equal to its curved surface area.

\[\therefore \]Required area\[=2\pi rh=2\times \frac{22}{7}\times 42\times 84\]

\[=22176\,\,c{{m}^{2}}\]