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Find the area and perimeter of the following from (i) Angle at the center={{60}^{\circ }}, Radius =4.2cm(ii) Angle at the center={{70}^{\circ }}, Radius =6cm
Class 10 | Frank | ICSE | Maths | Mensuration I
Find the area and perimeter of the following from (i) Angle at the center={{60}^{\circ }}, Radius =4.2cm(ii) Angle at the center={{70}^{\circ }}, Radius =6cm

(i)

According to question,

 Angle at the center ={{60}^{\circ }} radius =4.2cm,

Area of the sector =\left( \pi {{r}^{2}}\times \frac{\theta }{{{360}^{\circ }}} \right)

=\left[ \left( 22/7 \right)\times 4.22\times \left( {{60}^{\circ }}/{{360}^{\circ }} \right) \right]

=9.24c{{m}^{2}}

Perimeter of the sector =2r+\left( 2\pi r\times \theta /{{360}^{\circ }} \right)

=\left( 2\times 4.2 \right)+\left[ 2\times \left( 22/7 \right)\times 4.2\times \left( {{60}^{\circ }}/{{360}^{\circ }} \right) \right]

=8.4+4.4

=12.8cm

(ii)

According to question,

Angle at the centre ={{70}^{\circ }}

Radius =6cm,

Area of the sector =\left( \pi {{r}^{2}}\times \frac{\theta }{{{360}^{\circ }}} \right)

=\left[ \left( 22/7 \right)\times 62\times \left( {{70}^{\circ }}/{{360}^{\circ }} \right) \right]

=22c{{m}^{2}}

Perimeter of the sector =2r+\left( 2\pi r\times \theta /{{360}^{\circ }} \right)

=\left( 2\times 6 \right)+\left[ 2\times \left( 22/7 \right)\times 6\times \left( {{70}^{\circ }}/{{360}^{\circ }} \right) \right]

=12+7.33

=19.33cm

i

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