Question

The measure of a central angle of
a circle is 150 ° and radius of the
circle is 21 cm. Find the length of the arc and area of the sector associated with the central angle​

Answer 1

central angle 150 degree

radius21cm

length of arc=x2πr/360

= 150x2x22x21/360x7 = 55cm

.length of arc=55cm

Area of sector

Xπr 2/360

150x22x21x21/36ox 7 =577.50

Area Is577.50cm2

Answer 2

The length of an arch is 55 cm and area of sector is 577.5 sq. cm.

Step-by-step explanation:

Since we have given that

Measure of central angle = 150°

Radius of circle = 21 cm

So, the length of an arc would be

$\dfrac{\theta}{360^\circ}\times 2\pi r\\\\=\dfrac{150}{360}\times 2\times \dfrac{22}{7}\times 21\\\\=55\ cm$

now, the area of sector would be

$\dfrac{\theta}{360^\circ}\times \pi r^2\\\\=\dfrac{150}{360}\times \dfrac{22}{7}\times 21\times 21\\\\=577.5\ cm^2$

Hence, the length of an arch is 55 cm and area of sector is 577.5 sq. cm.

# learn more:

Find the area of a sector of a circle and length of minor arc of radius 21 cm and central angle 120 degree

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