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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)

Here, we have
r = 4 cm, ө = 30°
(i) Let OAPBO is a given sector, then

Here, we haver = 4 cm, ө = 30°(i) Let OAPBO is a given sector, then
Area of sector (OAPBO) = $πr squared space straight x space straight theta over 360$

= 3.14 x 4 x 4 x $30 over 360$
$fraction numerator 12.56 over denominator 3 end fraction space cm squared equals 4.19 space cm squared$

(ii) Area of major sector (unshaded part)
= Area of circle - Area of sector OAPBO
= (πr² - 4.19) cm²= (3.14 × 16 - 4.19) cm²= 46.05 cm²= 46.1 cm², (app.)

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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.

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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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