Question

answer me with solution please​

Answer 1

Answer:

Radius is 7 cm

Step-by-step explanation:

Area of the square = side × side

given Area = 121 cm²

Implies

s × s = 121

s = √121

s = 11 cm

Now total length of the wire = Perimeter of yhe square = 4 × side

= 4 × 11

= 44 cm

Now it is bent to form a circle

Therefore circumference of circle = length of wire

2 π r = 44

2 r = 44 × 7 / 22

2 r = 2 × 7

r = 7 cm

Answer 2

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept}}}$

Here the concept of area of square, perimeter of square, perimeter of circle and area of circle has been used. We see that we are given the area of a square ring. From that we can firstly find the side of the square ring and then its side. After that we will find the perimeter of the circular ring and then its radius. After finding this, we will find the area of the circular ring.

Let's do it !! _____________________________________________

★ Formula Used :-

$\\\;\boxed{\sf{\pink{Area\;of\;Square\;=\;\bf{(Side)^{2}}}}}$

$\\\;\boxed{\sf{\pink{Perimeter\;of\;Square\;=\;\bf{4\:\times\:Side}}}}$

$\\\;\boxed{\sf{\pink{Perimeter\;of\;Circle\;=\;\bf{2\pi r}}}}$

$\\\;\boxed{\sf{\pink{Area\;of\;Circle\;=\;\bf{\pi r^{2}}}}}$

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★ Solution :-

Given,

» Area of square = 121 cm²

• Let the radius of circle be r

~ For side of the Square ::

$\\\;\sf{\rightarrow\;\;Area\;of\;Square\;=\;\bf{(Side)^{2}}}$

By applying values, we get

$\\\;\sf{\rightarrow\;\;121\;=\;\bf{(Side)^{2}}}$

$\\\;\sf{\rightarrow\;\;Side\;=\;\bf{\sqrt{121}}}$

$\\\;\bf{\rightarrow\;\;Side\;=\;\bf{\red{11\;\;cm}}}$

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~ For Perimeter of Circle ::

Firstly, let's find the perimeter of square. This is given as,

$\\\;\sf{\rightarrow\;\;Perimeter\;of\;Square\;=\;\bf{4\:\times\:Side}}$

By applying values, we get

$\\\;\sf{\rightarrow\;\;Perimeter\;of\;Square\;=\;\bf{4\:\times\:11}}$

$\\\;\bf{\rightarrow\;\;Perimeter\;of\;Square\;=\;\bf{\orange{44\;\;cm}}}$

We know that the wire is bent in the form of square. So perimeter of square will be equal to the perimeter of circle. Then,

$\\\;\bf{\rightarrow\;\;Perimeter\;of\;Circle\;=\;\bf{\blue{44\;\;cm}}}$

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~ For the Area of Circle ::

We know that,

$\\\;\sf{\rightarrow\;\;Perimeter\;of\;Circle\;=\;\bf{2\pi r}}$

By applying values, we get

$\\\;\sf{\rightarrow\;\;44\;=\;\bf{2\:\times\:\dfrac{22}{7}\:\times\:r}}$

$\\\;\sf{\rightarrow\;\;r\;=\;\bf{\dfrac{44\:\times\:7}{2\:\times\:22}}}$

$\\\;\sf{\rightarrow\;\;r\;=\;\bf{\dfrac{44\:\times\:7}{44}}}$

$\\\;\sf{\rightarrow\;\;r\;=\;\bf{\green{7\;\;cm}}}$

Hence, we got the radius of circle. Now using the formula of area, we get

$\\\;\sf{\rightarrow\;\;Area\;of\;Circle\;=\;\bf{\pi r^{2}}}$

$\\\;\sf{\rightarrow\;\;Area\;of\;Circle\;=\;\bf{\dfrac{22}{7}\:\times\:(7)^{2}}}$

$\\\;\sf{\rightarrow\;\;Area\;of\;Circle\;=\;\bf{\dfrac{22}{7}\:\times\:7\:\times\:7}}$

$\\\;\sf{\rightarrow\;\;Area\;of\;Circle\;=\;\bf{22\:\times\:7}}$

$\\\;\bf{\rightarrow\;\;Area\;of\;Circle\;=\;\bf{\purple{154\;\:cm^{2}}}}$

This is the answer.

$\\\;\underline{\boxed{\tt{Area\;\:of\;\:circle\;=\;\bf{\purple{154\;\;cm^{2}}}}}}$

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★ More to know :-

$\\\;\sf{\leadsto\;\;Diagonal\;of\;Square\;=\;Side\sqrt{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Sector\;=\;\dfrac{\pi r^{2}\theta}{360^{\circ}}}$

$\\\;\sf{\leadsto\;\;Length\;of\;Chord\;=\;\dfrac{2\pi r\theta}{360^{\circ}}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Quadrant\;=\;\dfrac{\pi r^{2}}{4}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Semi\:-\:Circle\;=\;\dfrac{\pi r^{2}}{2}}$