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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

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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?

Here, r = 14 cm
and $angle AOB space equals space 90 degree$
$therefore space$ Area of minor sector

$equals fraction numerator 90 degree over denominator 360 degree end fraction straight x space πr squared equals 1 fourth straight x 22 over 7 straight x 14 straight x 14 equals space 154 space cm squared$

Here, r = 14 cmand Area of minor sector