Question

The perimeter of the sector OAB shown in the following figure, is
(a)$\frac{64}{3}cm$
(b)26 cm
(c)$\frac{64}{5}cm$
(d)19 cm​

Answer 1

Answer:

The perimeter of the sector , OAB is 64/3 cm .

Among the given options option (a) 64/3 cm is the correct answer.

Step-by-step explanation:

Given :  

Radius of a circle, r = 7 cm

Angle subtended by an Arc at the centre of a circle,θ = 60°

Perimeter of the sector ,P = length of the arc, AB + radius, OA + radius, OB

P = θ/360° × 2πr + r + r  

P = θ/360° × 2πr + 2 r  

P = 60°/360° × 2 × π× 7 + 2 × 7  

P = ⅙× 14 × 22/7 + 14  

P = 44/6 + 14

P = 22/3 + 14

P = (22 + 42)/3

P = 64/3 cm

Perimeter of the sector, OAB = 64/3 cm

Hence, the perimeter of the sector , OAB is 64/3 cm .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Solution:-

Given:-

Radius = 7 cm.

Angle (θ) = 60°

To Find :-

The perimeter of the sector OAB = ?

Find :-

Perimeter of Sector OAB = Length of arc (AB) + 2 × Radius.

=) Perimeter = θ/360°× 2πr + 2r

=) Perimeter = (60°/360°) × (2 × 22/7 × 7) + 2(7)

=) Perimeter = ¹/6 × 44 + 14

=) Perimeter = 22/3 + 14

=) Perimeter = ( 22 + 42)/3

=) Perimeter = 64/3 cm.

Hence,

The perimeter of the sector OAB is 64/3 cm.