Question 12 - Area of combination of figures : sector based - Chapter 11 Class 10 Areas related to Circles

Transcript

Question 12 In figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the quadrant OACB, It is given that, OACB is a quadrant Given radius = 3.5 cm We know that Area of Quadrant OACB = 1/4 Area of a circle Area of quadrant OACB = 1/4 2 = 1/4 22/7 (3.5)2 = 1/4 22/7 3.5 3.5 = 3.625 cm2 Question 12 In figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (ii) Shaded region Area of shaded region = Area of quadrant OACB Area of BOD We calculated Area of quadrant in part (i) Area of BOD Area of =1/2 Base Height Since OACB is a quadrant BOA = 90 Now, Area BOD = 1/2 Base Height = 1/2 OB OD = 1/2 3.5 2 = 3.5 cm2 Area of shaded region = Area of quadrant OACB Area of = 9.625 3.5 = 6.125 cm2 Hence, Area of shaded region = 6.125 cm2