Question : The area of the sector of a circle of radius 12 cm is $32 \pi \;\mathrm{cm}^2$. Find the length of the corresponding arc of the sector.
Option 1: $\frac{16}{3} \pi$ cm
Option 2: $\frac{13}{3} \pi$ cm
Option 3: $\frac{10}{3} \pi$ cm
Option 4: $\frac{8}{3} \pi$ cm
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $\frac{16}{3} \pi$ cm
Solution : Given: The radius of the circle is 12 cm. The area of the sector of a circle is $32\pi$ cm 2 . Area of the sector = $\pi r^2× \frac{\theta}{360^{\circ}}$ ⇒ $32\pi=\pi ×12^2×\frac{\theta}{360^{\circ}}$ ⇒ $\frac{\theta}{360}=\frac{32}{144}$ ⇒ $\frac{\theta}{360}=\frac{2}{9}$ Length of the arc = $2\pi r×\frac{\theta}{360^{\circ}}$ = $2\pi×12×\frac{2}{9}=\frac{16}{3} \pi$ cm So, the length of the arc is $\frac{16}{3} \pi$ cm. Hence, the correct answer is $\frac{16}{3} \pi$ cm.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : The radius of a circle with centre at O is 6 cm and the central angle of a sector is 40°. Find the area of the sector.
Question : The area of a sector of a circle of radius 28 cm is 112 cm2. Find the length of the corresponding arc of the sector.
Question : The area of a sector of a circle is 88 sq. cm., and the angle of the sector is 45°. Find the radius of the circle. (Use $\pi=\frac{22}{7}$)
Question : Two circles touch each other externally. The radius of the first circle with centre O is 12 cm. Radius of the second circle with centre A is 8 cm. Find the length of their common tangent BC.
Question : A circular arc whose radius is 4 cm makes an angle of 45º at the centre. Find the perimeter of the sector formed. (Take $\pi=\frac{22}{7}$)
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile