Question

a wire 56cm long is bent in the form of a circle. find the area it can enclose

Answer 1

$\large\sf\underline{Given}$

• Length of the wire = 56 cm .

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

• Area of the circle / Area that the wire encloses .

$\large\sf\underline{Solution}$

We know ,

$\small{\underline{\boxed{\mathrm\pink{Circumference\:of\:the\:circle=2πr}}}}$

$\sf➛\:Circumference\:of\:the\:circle=56$

$\sf➛\:2πr=56$

$\sf➛\:2 \times \frac{22}{7} \times r=56$

$\sf➛\:\frac{44}{7} \times r=56$

$\sf➛\:r=\frac{56 \times 7}{44}$

$\sf➛\:r=\frac{392}{44}$

${\sf{{\purple{➤\:r=8.9\:cm}}}}$

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Now ,

$\small{\underline{\boxed{\mathrm\pink{Area\:of\:the\:circle=πr^{2}}}}}$

$\sf➛\:πr^{2}$

$\sf➛\:\frac{22}{7} \times (8.9)^{2}$

$\sf➛\:\frac{22}{7} \times 8.9 \times 8.9$

$\sf➛\:\frac{22}{7} \times 79.21$

$\sf➛\:\frac{22}{7} \times \frac{7921}{100}$

$\sf➛\:\frac{174262}{700}$

${\sf{{\purple{➤\:248.84\:sq\:cm}}}}$

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