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Find the area and perimeter of the following from (iii) Angle at the center={{100}^{\circ }},, Diameter =42cm.
Class 10 | Frank | ICSE | Maths | Mensuration I
Find the area and perimeter of the following from (iii) Angle at the center={{100}^{\circ }},, Diameter =42cm.

(iii)

According to question,

Diameter =42cm, angle at the center ={{100}^{\circ }}

Radius = half of the diameter of the circle

r=d/2

r=42/2

r=21cm

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

=\left[ \left( 22/7 \right)\times 212\times \left( {{100}^{\circ }}/{{360}^{\circ }} \right) \right]

=385c{{m}^{2}}

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

=\left( 2\times 21 \right)+\left[ 2\times \left( 22/7 \right)\times 21\times \left( {{100}^{\circ }}/{{360}^{\circ }} \right) \right]

=42+36.66

=78.66cm

i

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