The length of an arc of a circle of radius 5cm is 4cm. Find the area of the sector

ijeoma16god

1 year ago

wtf
i don't understand

Maureen15

2 years ago

Length of the arc
(
l
)
=
θ
360
∘
×
2
π
r
…
(
i
)
where
θ
is the angle subtentded by the arc at the centre of the circle.

Area of the sector
(
A
)
=
θ
360
∘
×
π
r
2

Multiply and divide with 2 on the R.H.S.
⇒
A
=
θ
360
∘
×
2
π
r
2
×
1
2

⇒
A
=
(
θ
360
∘
×
2
π
r
)
×
r
×
1
2

⇒
A
=
l
×
r
2



(
from
(
i
)
)


Given,
l
=
4

cm
,
r
=
5

cm


∴
Area of the sector
(
A
)
=
4
×
5
2









































=
10


Hence, the area of the sector is
10

cm
2
.