Question

The side of a square is 10 cm. Find the area of circumscribed and inscribed circles.

Answer 1

Answer:

The Area of circumscribed circle is  157 cm² & Area of inscribed circle is 78.5 cm².

Step-by-step explanation:

SOLUTION :  

Given :  

Side of square ,a = 10cm

 

Radius of inscribed circle ,r = side/2 = 10/2 = 5 cm

Radius of inscribed circle ,r = 5cm

 

Area of inscribed circle ,A1 = πr²

A1 = 22/7 × 5²

A1 = 22/7 × 25  

A1 = (22 × 25)/7

A1 = 550/7

A1 = 78.57 cm²

Area of inscribed circle , A1= 78.5 cm²

 

Radius of circumscribed circle ,R = diagonal of square/2  = √2a/2

R = (√2 × 10)/2  =  5√2  

Radius of circumscribed circle ,R = 5√2 cm

 

Area of circumscribed circle, A2 = πR²

A2 = 22/7 × (5√2)²

A2 = 22/7 × 25 × 2

A2 =  (22 × 50)/7

A2 = 1100/7

A2 = 157 cm²

Area of circumscribed circle, A² = 157 cm²

 

Hence, the Area of circumscribed circle is  157 cm² & Area of inscribed circle is 78.5 cm².

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Answer 2

$\huge \boxed {\underline{{ \mathrm{Solution:}}}} \\ \\ \sf \underline{ \underline{Given : }} \\ \rm Side \: of \: a \: Square = \boxed { \boxed{ \text{10 cm}}} \\ \\ \sf\underline { \underline{Explanation : }} \\ \sf When \: it \: is \: Circumscribed : \\ \rm The \: Diameter \: will \: be \: Square \: Side \\ \sf \therefore r = \boxed { \boxed{ \text{5 cm}}} \\ \\ \rm Area \: of \: Circle :\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \pi r {}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \frac{22}{7} \times 5 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \boxed{ \boxed{ \sf 78.57 \: cm {}^{2}}} \\ \\ \\ \sf When \: it \: is \: Inscribed : \\ \rm T he \: Diameter \: will \: be \: its \: Diagonal \\ \therefore \rm r = \boxed{ \boxed{ \rm 5\sqrt{2} }} \\ \\ \rm Area \: of \: Circle : \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \pi r {}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \frac{22}{7} \times 5 \sqrt{2} \times 5 \sqrt{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \boxed{ \boxed{ \sf 157.14 \: cm {}^{2} }}$