Question

1.
A circular wire of radius 5cm is cut and bent again into an arc of a circle of
radius 10cm. The angle subtendended by the arc at the centre in radian is
1)
2)
3)
4)​

Answer 1

Given:

Radius of circular wire = 5cm

Radius of arc = 10cm

To Find:

Angle subtendended by the arc at the centre in radian

Solution:

Circumference of wire = 2πr

= 2×π×5 = 10π

ATQ

Wire is cut and bent again into an arc.

So length of arc = circumference of wire = 10π

Angle subtendended by the arc

= length of arc/ radius of arc

= 10π/10

= π radian

Hence, angle subtendended by the arc at the centre is π radian.

Answer 2

Step-by-step explanation:

Given :

• A circular wire of radius 5cm

• bent again into an arc of a circle of radius 10cm.

To Find :

• The angle subtendended by the arc at the centre in radian is

Solution :

Concept :

• The circumference is the distance around a closed curve. It is a special perimeter.

• The circumference of a circle means the distance around the boundary of a circle. It is given by the formula

• Circumference of a circle = 2Πr, where r is the radius of the circle.

$: \implies \: \: \: \: \: \boxed{ \sf Circumference \: m \: of \: wire = 2 \: \pi \: r}$

Substitute all value :

$: \implies \: \: \: \: \: \sf Circumference \: m \: of \: wire = 2 \: \times \pi \: \times 5 \\ \\ \\ : \implies \: \: \: \: \: \sf Circumference \: m \: of \: wire =10 \: \pi$

$\implies \: \: \: \: \: \boxed{ \sf Angle \: substended \: = \frac{length \: of \: arc}{radius \: of \: arc} } \:$

Substitute all values :

$\implies \: \: \: \: \: \sf Angle \: substended \: = \frac{10 \: \pi}{10} \: \\ \\ \\ \implies \: \: \: \: \: \sf Angle \: substended \: = \pi \: \\ \\ \\ \implies \: \: \: \: \: \sf Angle \: substended \: = \: 3.14$

Hence, angle subtendended by the arc at the centre is 3.14 radian.