CBSE Class 10 Maths (Basic) 2023 · Paper 430/C/1 · Question 36

Areas Related to Circles 4 marks Hard

Age of a tree: The most accurate way to determine the age of a tree is to count the annual rings of wood growth. To make an identification mark, the forest department has painted segment ACBA (see diagram). If chord AB makes an angle

9 0^{\circ}

at the centre and radius of the trunk is

21

cm, then find the following. (Use

π = \frac{22}{7}

)

Circle of radius 21 cm with chord AB subtending 90 deg at centre O

(i)Find the length of chord AB.[1]
(ii)Find the area of triangle OAB.[1]
(iii)(a)Find the area of segment ACBA.[2]
(iii)(b)OR Find the perimeter of sector OACBO.[2]

Answer

(i)

A B = 212 \approx 29.7

cm; (ii) Area of

△ O A B = 220.5

^{2}

; (iii)(a) Segment ACBA

= 126

^{2}

(or (iii)(b) Perimeter of sector

= 75

cm).

🔒 Step-by-step solution

From the board paper

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CBSE Class 10 Maths (Basic) 2023 · Paper 430/C/1 · Question 36

Answer

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