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RS Aggarwal Solutions Class 10 Mathematics Solutions for Area Of Circle Sector And Segment Exercise 16A in Chapter 16 - Area Of Circle Sector And Segment

Question 12 Area Of Circle Sector And Segment Exercise 16A

A chord 10 cm long is drawn in a circle whose radius is 5√2 cm. Find the areas of both segments. (Take pi = 3.14)

Answer:

Radius of circle = 5√2 cm

Chord = 10 cm

To find: Areas of both the segments

R S Aggarwal Solutions - Mathematics - Class 10 chapter Area Of Circle Sector And Segment Question 12 Solution image

R S Aggarwal Solutions - Mathematics - Class 10 chapter Area Of Circle Sector And Segment Question 12 Solution image

Now,

Area of minor segment = (area of sector OACBO) – (area of ∆OAB)

= 39.25 - 25 = 14.25 cm^2

Area of the major segment = (Area of circle) - (Area of minor segment)

\begin{array}{l} =\left(\frac{22}{7} \times 5 \sqrt{2} \times 5 \sqrt{2}-14.25\right) \mathrm{cm}^{2} \\ =\left(\frac{1100}{7}-14.25\right) \mathrm{cm}^{2}=(157-14.25) \mathrm{cm}^{2} \\ =142.75 \mathrm{cm}^{2} \end{array}

Therefore, Area of the major segment is 142.75 cm^2.

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