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.

Question

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.

Philoid · Accepted Answer

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.