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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.

Here, we have
r = 21 cm and ө = 120°
Let OACBO is the given sector and $stack bold A bold C bold B with bold overbrace on top$ is the given length of arc, then

Here, we haver = 21 cm and ө = 120°Let OACBO is the given sector an
(i) The length of the arc (ACB)

$equals space 2 πr space space straight x space straight theta over 360 equals space 2 space straight x space 22 over 7 space straight x space 21 space straight x space 120 over 360 equals space 44 space cm$
(ii) Area of sector (OACBO)

$πr squared space straight x space straight theta over 360 equals space 22 space straight x space 21 space equals space 462 space cm squared$