Book: RS Aggarwal - Mathematics
Chapter: 18. Area of Circle, Sector and Segment
Subject: Maths - Class 10th
Q. No. 32 of Exercise 18A
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32
In the given figure, the shape of the top of a table is that of a sector of circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm, then find the perimeter of the top of the table.
Give:
Radius of the circle = 42 cm
Central angle of the sector = ∠AOB = 90°
Perimeter of the top of the table = Length of the major arc AB + 2 × radius …………………. (i)
Length of major arc AB = 
× 2πr
= 
× 2 × 
× 42
= 
× 2 × 22 × 6
= 
× 264 = 3 × 66 = 198 cm
Thus, using (i), we have
Perimeter of the top of the table = 198 + 2 × 42
= 198 + 84 = 282 cm
Hence, the perimeter of the top of the table is 282 cm.
