Question

05 A piece of wire 20 cm is cut into two parts one of them being 7 cm long. Each part is bent to form a circle. The ratio of the area of larger circle to smaller circle is Mathem Q1 JE 169 49 13 7 39 28 Q5 Q9 Q1 23 43 Q13 Deselect Skip Next​

Answer 1

GIVEN -

Length of the wire = 20 cm

Length of the cut part = 7 cm

TO FIND -

The ratio of the area of larger to smaller circle

SOLUTION -  

Total length of the wire = 20 cm.

After cutting into two parts, length of one part is 7 cm

So the length of another part becomes = (20 - 7 ) cm = 13cm

When the wire is bent in the form of a circle, length of the wire becomes equal to the circumference of the circle.

we know, circumference of a circle = $2\pi r$ ( where r is radius of the circle)

For wire of length 7 cm

2 $\pi$$r_{1}$ = 7

∴ $r_{1}$   = $\frac{7}{2\pi }$

Thus area of the circle having radius $\frac{7}{2\pi }$  ( $A_{1}$ ) = $\pi r_{1} ^{2}$

                                                                           = $\pi (\frac{7}{2\pi }) ^{2}$

For wire of length 13 cm.            

$2\pi r_{2$ = 13

∴$r_{2} = \frac{13}{2\pi }$

Thus, area of the circle having radius $\frac{13}{2\pi }$  ( $A_{2}$ )  =     $\pi r_{2} ^{2}$

                                                                             =    $\pi (\frac{13}{2\pi } )^{2}$          

Now,

area of the circle having radius $\frac{13}{2\pi }$  ( $A_{2}$ )   :  area of the circle having radius $\frac{7}{2\pi }$  ( $A_{1}$ )  

                                     $\pi (\frac{13}{2\pi } )^{2}$                     :      $\pi (\frac{7}{2\pi }) ^{2}$

                                          169                     :   49

∴ The ratio of the area of larger to smaller circle is 169 : 49