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Areas Related to Circles

Short Answer Type

71. The numerical difference between circum-ference and diameter is 30 cm. What is the radius of the circle?

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72. If an arc forms 90° at the centre O of the circle, what is the ratio of its length to the circumference of the circle?

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73. Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding major segment. (use π = 3.14)

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74. Find the area of the segment of a circle of radius 14 cm, if the length of the corresponding arc APB is 22 cm. [Use π = 22/7]

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75. AB is a chord of a circle of radius 10 cm. The chord subtends a right angle at the centre of the circle. Find the area of the minor segment.

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76.

In a circle of radius 21 cm, an arc subtends an angle 60° at the centre. Find
(i)    the length of the arc
(ii)    area of the sector formed by the arc.
(iii)    area of the segment formed by the corresponding chord.

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77. A sector is cut off from a circle of radius 21 cm. The angle subtended at centre is 120°, find the length of its arc and the area.

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78. A pendulum swings through an angle 30° and describes an arc 8.8 cm in length. Find the length of the pendulum

open parentheses Use space equals space 22 over 7 close parentheses.

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79. The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by minute hand in 35 minutes.

Angle described by the minute hand in 60 minutes = 360°.
Angle described by the minute hand in 35 minutes

$equals space 360 over 60 space straight x space 35 space equals space 210 degree$
Thus, we have,

$straight theta$ = 210 $degree$ , and r = 12 cm.
Therefore, required area
$equals space πr squared space straight x space straight theta over 360 equals space space open square brackets 22 over 7 straight x space 12 space straight x space 12 space straight x space 210 over 360 close square brackets space cm squared equals space 264 space cm squared$

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80.

Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centres is 14 cm. Find the radii of the circle.

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