Question

A cow is tied to a post by a rope 30 m long. If the cow moves along the circumference of a
circle always keeping the rope tight, how far will it have gone
has traced angle of 105​

Answer 1

Answer:

• When the rope has traced an angle of 105°, a cow will have gone 55 m far.

Step-by-step explanation:

Given that:

• A cow is tied to a post by a rope 30 m long.
• The cow moves along the circumference of a circle always keeping the rope tight.
• The rope has traced an angle of 105°.

To Find:

• How far will it have gone when the rope has traced an angle of 105°?

Formula used:

• Length of an arc = 2πrθ/360°
• Length of an arc = (2 × 22 × rθ)/(7 × 360°)

Where,

• θ = Angle formed by an arc
• r = Radius of a circle

We have:

• θ = 105°
• r = 30 m

Finding the distance covered by a cow:

⟶ Length of an arc = (2 × 22 × 30 × 105)/(7 × 360)

⟶ Length of an arc = 138600/2520

⟶ Length of an arc = 55

∴ The distance covered by a cow = 55 m

Answer 2

Answer:

Given :-

• A cow is tied to a post by a rope 30 m long. The cow moves along the circumference of a circle always keeping the rope tight. The rope has traced angle of 105°.

To Find :

• How far will it have gone.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Length\: of\: an\: arc =\: 2{\pi}r\bigg(\dfrac{{\theta}}{360^{\circ}}\bigg)}}}$

where,

• r = Radius
• $\pi$ = Angle form by arc

Solution :-

Given :

• Angle form by arc = 105°
• Radius = 30 cm

According to the question by using the formula we get :

$\implies \sf Length\: of\: an\: arc =\: 2 \times \dfrac{22}{7} \times 30\bigg(\dfrac{105}{360}\bigg)$

$\implies \sf Length\: of\: an\: arc =\: \dfrac{1320}{7} \times \sf \dfrac{105}{360}$

$\implies \sf Length\: of\: an\: arc =\: \dfrac{\cancel{138600}}{\cancel{2520}}$

$\implies \sf\bold{\red{Length\: of\: an\: arc =\: 55\: m}}$

$\therefore$ 55 m far will it have gone.