10th Class Mathematics Areas Related to Circles Question Bank MCQs - Areas Related to Circles

A circular wire of radius \[\text{42 cm}\] is cut and bent into the form of a rectangle whose sides are in the ratio of\[\text{6}:\text{5}\]. The smaller side of the rectangle is:

A) \[30\,cm\]

B) \[60\,cm\]

C) \[70\,cm\]

D) \[80\,cm\]

Correct Answer: B

Solution :

[b] Length of wire

\[=2\pi \times 42=2\times \frac{22}{7}\times 42=264cm\]

Let side are \[6x\] and \[5x\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2(6x+5x)=264\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11x=132\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,x=12\]

\[\therefore \] Smaller side \[=12\times 5=60\,cm.\]