What is the area of the sector of a circle with radius $5 cm$ and central angle $3 0^{\circ}$ ?

easy MCQ 2 marks Class 10 · Mathematics · Areas Related to Circles

Answer

\frac{25 π}{12} cm^{2}

The correct answer is $\frac{25 π}{12} cm^{2}$ — Hence $A = \frac{25 π}{12} cm^{2}$ .

Step-by-step solution

Sector area formula: $A = \frac{θ}{360} \times π r^{2}$ .
Substitute $θ = 3 0^{\circ}$ and $r = 5 cm$ : $A = \frac{30}{360} \times π \times 5^{2}$ .
Simplify the fraction $\frac{30}{360} = \frac{1}{12}$ and compute $5^{2} = 25$ : $A = \frac{1}{12} \times 25 π$ .
Hence $A = \frac{25 π}{12} cm^{2}$ .

Common mistake: Dividing by 180 instead of 360 when using the sector area formula.

Concept tested: sector area