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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.

Here, we have
ө = 90°, r = 10 cm

Here, we haveө = 90°, r = 10 cmArea of AOB = Area of sector OACBO
Area of $increment$ AOB = $1 half straight r squared space sin space straight theta equals space 1 half straight x space 10 space straight x space 10 space straight x space sin space 90 degree equals space 1 half space straight x space 10 space straight x space 10 space straight x space 1 space equals space 50 space cm squared space$
Area of sector OACBO

$space space space space space equals space πr squared space straight x space straight theta over 360 space space space space space equals space open parentheses 22 over 7 straight x space 10 space straight x space 10 space straight x space 90 over 360 close parentheses space cm squared space space space space space equals space open parentheses fraction numerator 11 space straight x space 10 space straight x space 10 over denominator 7 end fraction close parentheses space cm squared space space space space space equals space 550 over 7 space equals space 78.57 space cm squared$

Now,
Area of minor segment (ACBA)
= Area of Sector OACBO - Area of ∆AOB = (78.57- 50) cm²= 28.57 cm².

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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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