Question

Find the length of an arc of a circle of radius 7 cm which subtends an angle of 75° at the centre of the circle. Also, find the area of the corresponding sector.​

Answer 1

Given:

Radius of the circle = 7 cm

Angle at the centre is 75°.

To find:

Length of the arc and area of the sector.

Solution:

1) Formula to find the length of the arc is given by:

• Ф = L/r

here we take Ф in radian.

Ф = 75° ( in degrees)

Ф = 75×π/180

  = 5π/12

• Ф = L/r

• 5π/12 = L / 7

• 5/12 ×22/7 × 7 = L

• L = 55/6 cm

• L = 9.17 cm.

2) Area of the sector = Ф/360 πr²

                                  = 75/360 × 22/7 ×7 ×7

                                  = 385/12

                                  = 32.08 cm²

Length of the arc and area of the sector are 9.17 cm and 32.08 cm² respectively.

Answer 2

Answer:

length of the arc=35π/12 cm.

area of sector=245π/24 cm.sq.