Question

difference of radii of two circles are 7cm & their differences of their area are 7062cm².find the radius of two circles​

Answer 1

Step-by-step explanation:

The radius of two circle will be = " 43 cm "

Hope, it's help you.

Answer 2

$\large\underline{\sf{Solution-}}$

$\sf \: Let \: C_1 \: and \: C_2 \: be \: two \: circles \: having \: radius \: R \: and \: r$

$\sf \: such \: that \: R \: > \: r$

According to statement,

• Difference of the radius of two circles is 7 cm.

$\bf :\longmapsto\:R - r \: = \: 7 - - - (1)$

We know,

$\: \: \: \boxed{ \sf \: Area_{(circle)} = \pi \: {r}^{2} }$

According to statement,

• Difference of their areas = 7062

$\rm :\longmapsto\:\pi \: {R}^{2} - \pi \: {r}^{2} = 7062$

$\rm :\longmapsto\:\pi \: ( {R}^{2} - {r}^{2} ) = 7062$

$\rm :\longmapsto\:\dfrac{22}{7} (R + r)(R - r) = 7062$

$\rm :\longmapsto\:\dfrac{22}{ \cancel7} (R + r)( \cancel7) = 7062$

$\bf\implies \:R + r = 321 - - - (2)$

On adding equation (1) and equation (2), we get

$\rm :\longmapsto\:2R = 328$

$\rm :\implies\: \: \: \boxed{ \bf \: R = 164 \: cm \: }$

On substituting the value of R in equation (1), we get

$\rm :\longmapsto\:164 - r = 7$

$\rm :\implies\: \: \: \boxed{ \bf \: r = 157 \: cm \: }$

Additional Information :-

$1. \: \: \: \boxed{ \sf \: Area_{(rectangle)} = Length \times Breadth}$

$2. \: \: \: \boxed{ \sf \: Perimeter_{(rectangle)} = 2(Length + Breadth)}$

$3. \: \: \: \boxed{ \sf \: Area_{(square)} = {(side)}^{2} }$

$4. \: \: \: \boxed{ \sf \: Perimeter_{(square)} = 4 \times side}$

$5. \: \: \: \boxed{ \sf \: Perimeter_{(circle)} = 2\pi \: r}$