# The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively 120° and 40°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you - Mathematics

Sum

The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively 120° and 40°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe?

#### Solution

Let the lengths of the corresponding arc be l1 and l2.

Radius of the sector PO1QP = 7 cm

Radius of the sector AO2BA = 21 cm

And, Central angle of sector PO1QP = 120°

Central angle of sector AO2BA = 40°

Area of sector with angle O_1 = (pir^2)/360 xx 120

= (pi7^2)/360 xx 120

= 154/3  cm^2

Area of sector with angle O_2 = (pir^2)/360 xx 40

= (pi(21)^2)/360 xx 40

= 154 cm2

Arc length of sector PO1QP = Central angle × radius

= 120 xx 7 xx pi/180

= 44/3 cm

Arc length of sector AO2BA = Central angle × radius

= 40 xx 21 xx pi/180

= 44/3 cm

Hence, we observe that arc lengths of two sectors of two different circles may be equal but their area need not be equal.

Concept: Areas of Sector and Segment of a Circle
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.4 | Q 16 | Page 135
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