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Areas Related to Circles

Short 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

Let r₁ = 7 cm (for sector OCDO) and r₂ = 21 (for sector OBAO)
r₂ (for sector OABO) = 21 cm
and, ө = 30°

Now, Area of sector (OCDO)

$equals space πr squared straight x straight theta over 360 equals space 22 over 7 straight x space 7 space straight x space 7 space straight x space 30 over 360 equals space 231 over 2 space cm squared$
and, Area of sector (OABO)

$equals space πr squared space straight x space straight theta over 360 equals space 22 over 7 straight x space 21 space straight x space 21 space straight x space 30 over 360 equals space space 77 over 6 space cm squared$
Hence, required area |(shaded part)
= Area of sector (OCDO) - Area of sector (OABO)

$space space equals space open parentheses 231 over 2 minus 77 over 6 close parentheses space cm squared space space equals space open parentheses fraction numerator 693 minus 77 over denominator 6 end fraction close parentheses space cm squared space space equals space 616 over 6 equals 308 over 3 space cm squared$

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Long 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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Short 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.

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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

Long Answer Type

Short Answer Type

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