Question

a copper wire when bent in the form of square encloses an area of 121cm. if the same wire is bent into the form of a circle , find the area of the circle

Answer 1

Heya mate,
nice question
Here is your answer

Area of the square = 121cm²
side² = 121
side = √121 = 11cm
So we got the side of the square 11cm

if the same wire is bent into a circlr, then
perimeter of the square = circumference of the circle.
So perimeter of the square
$= 4 \times sides \\ = 4 \times 11 \\ = 44cm$
Hence the circumference of the circle = 44cm
$2\pi \: r = 44 \\ = > 2 \times \frac{22}{7} \times r = 44 \\ = > r = 44 \times \frac{1}{2} \times \frac{7}{22} \\ \: \: \: \: \: \: \: \: \: \: \: \: = 7cm$
Hence we found the radius of the circle 7cm

So area of the circle is
$= \pi \: {r}^{2} \\ = \frac{22}{7} \times {7}^{2} \\ = \frac{22}{7} \times 7 \times 7 \\ = 22 \times 7 \\ = 154cm {}^{2}$

Hence the area of the circle is 154cm²

Hope this helps

if you have any doubts or want any help, you can ask me. i would really love to help.

Thank you

#Sneha
☆ Brainly Benefactor ☆

Answer 2

Hey!

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According to the Question,

Area of the square= 121 cm^2
Area of square= side×side
Side of square= √121
Side of square= 11 cm

If this wire is bent into circle then,

Perimeter of square = Circumference of circle
Perimeter of square= 4 × side
= 4×11
= 44 cm

Thus, circumference of circle= 44 cm
Circumference of circle= 2πr

Circumference= 2×22/7×r
44= 2×22/7×r
r= 44×1/2×7/22
r=7cm

Area of circle= πr^2
Area= 22/7×7/7
Area= 154 cm^2

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Hope it helps...!!!