An arc of a circle is of length 5π cm and the sector it bounds

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 Multiple Choice QuestionsShort Answer Type

31.

In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB, (ii) shaded region. 

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32.

In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14).


Fig. 12.31

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33.

AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠ AOB = 30°, find the area of the shaded region.


Fig. 12.32

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 Multiple Choice QuestionsLong Answer Type

34.

In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region. 


Fig. 12.33

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 Multiple Choice QuestionsShort Answer Type

35.

Calculate the area of the designed region in Fig. 12.34 common between the two quadrants of circles of radius 8 cm each.


Fig. 12.34

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36. A chord of a circle of radius 14 cm subtends a right angle at the centre. What is the area of the minor sector?
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37. A chord of a circle of radius 14 cm subtends 60° at the centre. Find the area of the major sector.
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38. What is the perimeter of a sector of angle 45° of a circle with radius 7 cm ? [Use π = 22/7].  
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39. In the following figure, the length of an arc AB = 20π cm is a sector of a circle, find the radius of the circle.


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40. An arc of a circle is of length 5π cm and the sector it bounds has an area 20π cm2. Find the radius of the circle.


We know that
Area of a sector bounded by a given arc equals 1 half x (length of a given arc) × radius of a circle
rightwards double arrow space space straight A space equals space 1 half lr space rightwards double arrow space 20 straight pi space equals space 1 half space straight x space 5 straight pi space straight x space straight r
rightwards double arrow space space straight r space equals space fraction numerator 40 straight pi over denominator 5 straight pi end fraction equals space 8 space cm

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