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Areas Related to Circles

Long Answer Type

171.

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

172.

In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. $(Use π = \frac{22}{7})$

173.
In the given figure, O is centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region.

AC = 24 cm, AB = 7 cm

Since BC is the diameter of the circle,

$So, ∠ BAC = 90 ° In right ∆ BAC, {BC}^{2} = {AC}^{2} = {AB}^{2} \Rightarrow {BC}^{2} = 24^{2} + 7^{2} \Rightarrow {BC}^{2} = 625 \Rightarrow BC = 25 So, the radius of the circle = OC = 12.5 cm Area of the shaded region = Area of the circle - Area of ∆ BAC - Area of sector CD = {πr}^{2} - \frac{1}{2} x AB X AC - \frac{θ}{360} X {πr}^{2} = (\frac{22}{7} x 12.5 x 12.5) - (\frac{1}{2} x 7 x 24) - (\frac{90}{360} x \frac{22}{7} x 12.5 x 12.5) . . . . . . . . . . (∵ ∠ BOD = 90 ° \Rightarrow ∠ COD = 90 °) = 491.07 - 84 - 122.77 = 284.3 {cm}^{2} (approximately) Hence, the area of the shaded region is 284.3 {cm}^{2} approximately .$

Multiple Choice Questions

174.

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is

Long Answer Type

175.

In fig., OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. $[Use π = \frac{22}{7}]$

176.

In fig., PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm and centre O. If $∠$ POQ = 30⁰, then find the area of the shaded region.