Question

The perimeter of the sector of a circle of area 36 pi sq.cm is 28 cm .The area of sector is equal to

Answer 1

$Let \: radius \: of \: the \: circle = r \:cm$

$length \: of \: arc = l \:cm$

$and \: sector \: angle = \theta$

$i) Area \:of \:the \: circle = 36 \:\pi cm^{2}$

$\implies \pi r^{2} = 36 \:\pi cm^{2}$

$\implies r^{2} = \frac{36 \:\pi cm^{2} }{\pi }$

$\implies r^{2} = 36$

$\implies r = 6 \:cm \: --(1)$

$ii) Perimeter \: of \: the \: sector = 28 \:cm$

$\implies l + 2r = 28 \:cm$

$\implies l + 2\times 6 = 28 \:cm \: \blue { [ From \: (1) ]}$

$\implies l = 28 - 12$

$\implies l = 16 \:cm \: --(2)$

$iii) \frac{\theta}{360} \times 2\pi r = 28$

$\implies \theta = \frac{28 \times 360}{2 \pi r}$

$\implies \theta = \frac{28 \times 360}{2\pi\times 6 }$

$\implies \theta = \frac{28 \times 30}{\pi } \: --(3)$

$Now, \red{Area \: of \: a \: sector }$

$=\frac{\theta }{360} \pi r^{2}$

$= \frac{\frac{28 \times 30}{\pi }}{360} \times 36 \pi$

$= 28 \times 3$

$= 84 \:cm^{2}$

Therefore.,

$\red{Area \: of \: a \: sector } \green { =84 \:cm^{2}}$

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Answer 2

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