Question

Find the radius and perimeter of a circle whose area is 77cm².

Answer 1

area=πr²
77=22/7r²
77×7=22r²
539=22r²
539/22=r²
24.5=r²
r=√24.5
r=4.94cm

radius=4.94cm

perimeter/circumference=2πr
=2×22/7×4.94
=31.05 cm(approx)

Answer 2

$\underline{\underline{\sf{ \color{fuchsia}{Given :} }}}$

Area of the semicircle = 77 cm²

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$\underline{\underline{\sf{ \color{fuchsia}{To\:Find :} }}}$

Perimeter of the circle

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$\underline{\underline{\sf{ \color{fuchsia}{Solution :} }}}$

$\underline{\bf{As\:we\:know\:that,}}$

$\star\:{\boxed{\sf{\color{fuchsia}{Area \: of \: circle = 2 \times Area \: of \: semicircle}}}}$

$: \: \implies \sf{Area \: of \: circle = 2 \times 77cm^{2} }$

$: \: \implies \sf{Area \: of \: circle =154 \: {cm}^{2} }$

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$\underline{\bf{Now, \: we\:know\:that,}}$

$\star\:{\boxed{\sf{\color{fuchsia}{Area \: of \: circle = \pi r^{2}}}}}$

$: \: \implies \sf{ 154 = \dfrac{22}{7} \times {r}^{2} }$

$: \: \implies \sf{ 7 \times 7 = {r}^{2} }$

$: \: \implies \sf{ 49 = {r}^{2} }$

$: \: \implies \sf{ {r}^{2} = 49 }$

$: \: \implies \sf{ {r} = \sqrt{ 49} }$

$: \: \implies \sf{ {r} = { 7 cm} }$

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$\underline{\bf{Now, \: we\:know\:that,}}$

$\star\:{\boxed{\sf{\color{fuchsia}{Perimeter = \pi r + 2r }}}}$

$: \: \implies \sf{ Perimeter = \dfrac{22}{7} \times 7 + 2 \times 7 }$

$: \: \implies \sf{ Perimeter = 22 + 14 }$

$: \: \implies \sf{ Perimeter = 36 }$

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$\color{fuchsia} \sf \therefore \: perimeter \: of \: the \: circle = 36cm \\ \color{fuchsia} \sf and \: radius = 7 cm$