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:
Given, radii of two circles are 7 cm and 21 cm
Central angle of the two angles are 120° and 40°
We have to find the areas of the sectors as well as the lengths of the corresponding arcs.
Considering radius = 7 cm and central angle = 120°
Area of sector = πr²θ/360°
= (22/7)(7)²(120°/360°)
= (22)(7)(1/3)
= 154/3
= 51.33 cm²
Length of the arc = θ/360°(2πr)
= (120°/360°)(2)(22/7)(7)
= (1/3)(44)
= 44/3
= 14.67 cm²
Considering radius 21 cm and central angle = 40°
Area of sector = (22/7)(21)²(40°/360°)
= (22)(3)(21)(1/9)
= (22)(21)(1/3)
= (22)(7)
= 154 cm²
Length of the arc = θ/360°(2πr)
= (40°/360°)(2)(22/7)(21)
= (1/9)(44/7)(21)
= (1/9)(44)(3)
= 44/3
= 14.67 cm²
Therefore, we observe that the length of the arc of two circles are equal but the area of the sectors are not equal.
✦ Try This: The central angles of two sectors of circles of radii 9 cm and 28 cm are respectively 100° and 60°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe?
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 16
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
Summary:
The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively 120° and 40°. The areas of the two sectors are 51.33 cm² and 154 cm². The lengths of the corresponding arcs are 14.67 cm². We observe that the length of the arc of two circles are equal but the area of the sectors are not equal
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