Question
Find the area of a sector with a central angle of 150° in a circle with a radius of 12 cm.
The correct answer is
$60\pi\ cm^2$
Given:
- Radius: r = 12 cm
- Central angle: θ = 150°
Formula for the area of a sector:
A = (θ / 360°) × π r2
Step-by-step Calculation
A = (150 / 360) × π × (12)2
= (5 / 12) × π × 144
= 60π
Final Answer:
A = 60π cm2
Correct Option: Option 4 — 60π cm2.
Was this answer helpful?
Important Questions from 2-D Mensuration
- The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field? Take $\pi = \frac{22}{7}$
- The area of a square is $2304$ cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
- The length of a rectangular pitch is 30 m more than its breadth. Its area is $18,271$ m$^{2}$. Its breadth (in m) is:
- In a circle of radius 10.5 cm, if the angle of a sector is $\frac{2\pi}{3}$, then the perimeter of the sector is (in cm):
(Take $\pi = \frac{22}{7}$)
Need Expert Advice?
