Question : In the following figure, the length of arc AB is equal to five times the radius $r$ of the circle. Find the area of sector AOB.
Option 1: $2.5 r^2$
Option 2: $\frac{1}{2}r^2$
Option 3: $3r^2$
Option 4: $2r^2$
Latest: SSC CGL 2024 final Result Out | SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL Tier 1 Scorecard 2024 Released | SSC CGL complete guide
Suggested: Month-wise Current Affairs | Upcoming Government Exams
Correct Answer: $2.5 r^2$
Solution : Length of the arc AB = $5r$ Radius of the circle = $r$ Given: Length of arc = $5r$ ⇒ $\frac{\theta}{360^\circ }\times 2\pi r=5r$ ⇒ $\theta = \frac{360^\circ}{2\pi} \times 5$ Area of sector with angle $\theta$ = $\frac{\theta}{360^\circ}\pi r^2$ =$\frac{\frac{360^\circ}{2\pi} \times 5}{360^\circ}\pi r^2$ = $2.5r^2$ Hence, the correct answer is $2.5r^2$.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : The following formula is used to calculate which of the following? $\frac{\text { Angle of arc at centre }}{360°} \times \pi \times \text{Diameter}$
Option 1: Length of a sector
Option 2: Area of an arc
Option 3: The radius of a circle
Option 4: Length of an arc
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.
Option 1: 4 cm
Option 2: 8 cm
Option 3: 6 cm
Option 4: 5 cm
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
Question : In the given figure, PQR is a quadrant whose radius is 7 cm. A circle is inscribed in the quadrant as shown in the figure. What is the area (in cm2) of the circle?
Option 1: $385-221\sqrt{2}$
Option 2: $308-154\sqrt{2}$
Option 3: $154-77\sqrt{2}$
Option 4: $462-308\sqrt{2}$
Question : What is the area of the sector of a circle of radius 8 cm and formed by an arc of length 12 cm?
Option 1: 45 cm2
Option 2: 47 cm2
Option 3: 48 cm2
Option 4: 84 cm2
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile