What is the area (in cm
2
) of a sector of a circle, with central angle 75
∘
, when the diameter of the circle is 9cm?
- A185 \pi/32
- B135 \pi/16
- C185 \pi/16
- D135 \pi/32
Solution & Step-by-step Explanation
Given:
Diameter=9cm⟹Radius (r)=
2
9
cm
Central angle (θ)=75
∘
The formula for the area of a sector of a circle is:
Area=
360
∘
θ
×πr
2
Substitute the values:
Area=
360
75
×π×(
2
9
)
2
Area=
24
5
×π×
4
81
Area=
8×4
5×27×π
=
32
135π
cm
2
Diameter=9cm⟹Radius (r)=
2
9
cm
Central angle (θ)=75
∘
The formula for the area of a sector of a circle is:
Area=
360
∘
θ
×πr
2
Substitute the values:
Area=
360
75
×π×(
2
9
)
2
Area=
24
5
×π×
4
81
Area=
8×4
5×27×π
=
32
135π
cm
2