Question

In the adjoining figure the area enclosed between the concentric circles is 770 cm square. lf the radius of the outer circle is 21 cm , calculate the radius of inner circle.​

Answer 1

$\sf\large\underline{Given:}$

$\rm{\implies Difference\:area\:_{(outer\:circle-inner\:circle)}=770cm^2}$

$\rm{\implies Outer\:_{(radius\:of\:circle)}=21cm}$

$\sf\large\underline{To\: Find:}$

$\rm{\implies Inner\:_{(radius\:of\:circle)}=?}$

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

$\tt{\implies Let,\:the\: inner\: radius\:of\:circle\:be\:r}$

$\sf\large\underline{Formula\:used:}$

$\tt{\implies Area\:_{(circle)}=\pi\:r^2}$

$\tt{\implies Outer\:_{(area)}-Inner\:_{(area)}=Difference\:_{(area)}}$

$\tt{\implies \dfrac{22}{7}\times\:21^2-\dfrac{22}{7}\times\:r^2=770}$

• we take common here 22/7 here]

$\tt{\implies \frac{22}{7}\bigg(21^2-r^2\bigg)=770}$

$\tt{\implies 441-r^2=770\div\dfrac{22}{7}}$

$\tt{\implies 441-r^2=770\times\dfrac{7}{22}}$

$\tt{\implies 441-r^2=245}$

$\tt{\implies -r^2=245-441}$

$\tt{\implies -r^2=-196}$

$\tt{\implies r^2=196}$

$\tt{\implies r=\sqrt{196}=14cm}$

$\bf\large{Hence,}$

$\rm{\implies Inner\:_{(radius\:of\:circle)}=14cm}$

Answer 2

Solution:-

As we know that,

Area of circle=πr²

=>22/7×21²-22/7r²=770

22/7(21²-r²)=770

441-r²=770×7/22

441-r²=245

-r²=245-441

-r²=-196

r=14

therefore, inner radius of circle=14cm