Class 10 NCERT Maths Solution Exercise-12.2, Areas Related to Circles

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Question 12:

To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships warned. [Use π = 3.14]

It can be observed from the figure that the lighthouse spreads light across a

sector of 80° in a circle of 16.5 km radius.

Area of sector OACB =
                                        

Question 13:

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs.0.35 per cm². [Use √3 = 1.7]

It can be observed that these designs are segments of the circle.
Consider segment APB. Chord AB is a side of the hexagon. Each chord will substitute
360°/6 = 60° at the centre of the circle.

In ΔOAB,
∠OAB = ∠OBA (As OA = OB)
∠AOB = 60°
∠OAB + ∠OBA + ∠AOB = 180°
2∠OAB = 180° − 60° = 120°
∠OAB = 60°
Therefore, ΔOAB is an equilateral triangle.
Area of ΔOAB =
                             
 
 = 333.2 cm²
Area of sector OAPB =
                                         

Area of segment APB = Area of sector OAPB − Area of ΔOAB

Cost of making 1 cm² designs = Rs 0.35

Cost of making 464.76 cm² designs = 

= Rs 162.68

Therefore, the cost of making such designs is Rs 162.68.

Question 14:

Tick the correct answer in the following:

Area of a sector of angle p (in degrees) of a circle with radius R is

(A) , (B) , (C) , (D)

We know that area of sector of angle θ =
                                                            

Area of sector of angle P =

Hence, (D) is the correct answer.

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