The circumferences of two circles are in the ratio $3 : 4.$ The ratio of their areas is:
- A$3 : 4$
- B$4 : 3$
- ✓$9 : 16$
- D$16 : 9$
Answer: C.
View full solution →Question types
Area of Circle, Sector and Segment question types
164 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
164
Questions
5
Question groups
5
Question types
01
M.C.Q (1 Marks)
30 Q→022 Marks Questions
42 Q→033 Marks Question
28 Q→044 Marks Questions
35 Q→055 Marks Question
29 Q→Sample Questions
Area of Circle, Sector and Segment questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The length of an arc of the sector of angle $\theta^\circ$ of a circle with radius $R$ is:
- A$\frac{2\pi\text{R}\theta}{180}$
- ✓$\frac{2\pi\text{R}\theta}{360}$
- C$\frac{\pi\text{R}^2\theta}{180}$
- D$\frac{\pi\text{R}^2\theta}{360}$
Answer: B.
View full solution →The length of the minute hand of a clock is $21\ cm$. The area swept by the mmute hand in $10$ minutes is:
- ✓$231\ cm^2$
- B$210\ cm^2$
- C$126\ cm^2$
- D$252\ cm^2$
Answer: A.
View full solution →If the sum of the areas of two circles with radii $R1$ and $R2$ is equal to the area of a circle of radius $R$, then:
- A$\text{R}_1+\text{R}_2=\text{R}$
- B$\text{R}_1+\text{R}_2<\text{R}$
- C$\text{R}_1^2+\text{R}_2^2<\text{R}^2$
- ✓$\text{R}_1^2+\text{R}_2^2=\text{R}^2$
Answer: D.
View full solution →If the circumference of a circle and the perimeter of a square are equal, then:
- AArea of the circle $=$ area of the square
- ✓$($area of the circle$) > ($area of the square$)$
- C$($area of the circle$) < ($area of the square$)$
- DNone of these
Answer: B.
View full solution →In the given figure, an equilateral triangle has been inscribed in a circle of radius 4cm. Find the area of the shaded region. $\big[\text{Take }\pi=3.14\text{ and }\sqrt{3}=1.73.\big]$
View full solution →The difference between the circumference and radius of a circle is 37cm. Using $\pi=\frac{22}{7},$ find the circumference of the circle.
View full solution →The radii of two circles are 19cm and 9cm Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
The perimeter of a sector of a circle of radius 5.6cm is 27.2cm. Find the area of the sector.
The area of the sector of a circle of radius $10.5\ cm$, is $69.3\ cm^2$.
Find the central angle of the sector.
View full solution →Find the central angle of the sector.
The circumference of a circle exceeds its diameter by 45cm. find the circumference of the circle. $\Big[\text{Use }\pi=\frac{22}{7}\Big]$
View full solution →Find the lengths of the arcs cut off from a circle of radius 12cm by a chord 12cm long. Also, find the area of the minor gment. $\big[\text{Take }\pi=3.14\text{ and }\sqrt{3}=1.73.\big]$
View full solution →In the given figure, find the area of the shaded region, if ABCD is a square of side 14cm and APO and BPC are semicircles.
Find the area of the sector of a circle having radius $6\ cm$ and of angle $30^\circ $. $\big[\text{Take }\pi=3.14\big]$
View full solution →The wheels of a car make 2500 revolutions in covering a distance of 4.95km. Find the diameter of a wheel.$\Big[\text{Use }\pi=\frac{22}{7}\Big]$
View full solution →Find the area of a quadrant of a circle hose circumference is 44cm.
Four equal circles, each of radius 5cm, touch each other, as shown in the figure. Find the area included between them. $[\text{Take }\pi\ =3.14]$
View full solution →Find the perimeter of the s ded region in the figure, if ABCD is a square of side 14cm and APB and CPD are semicircles.
The side of a square is 10cm. Find (i) the area of the inscribed circle, and (ii) the area of the circumscribed circle. $[\text{Take }\pi\ =3.14]$
View full solution →In the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7cm and 3.5cm with centre 0. If $\angle\text{POQ}=30^\circ,$ find the area of the shaded region.
View full solution →The area of an equilateral triangle is $49\sqrt{3}\text{cm}^2.$ taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles. $\big[\text{Take }\sqrt{3}=1.73\big]$
View full solution →A racetrack is in the form of a ring whose inner circumference is 352m and outer circumference is 396m. Find the Width and the area of the track.
With the vertices $A, B$ and $C$ of a tringle $A B C$ as centres, arcs are drawn with radii $5 cm$ each as shown in the given figure. If $A B=14 cm, B C=48 cm$ and $C A=50 cm$ then find the area of the shaded region. [Use $\pi=3.14$ ]
View full solution →In the given figure, $ABCD$ is a rectangle with $\text{AB}=80\text{cm}$ and $\text{BC}=70\text{cm},$ $\angle\text{AED}=90^\circ$ and $\text{DE}=42\text{cm}$ A semicircle is dn wn, taking BC as diameter. Find the area o the shaded region.
View full solution →If three circles of radius a each, drawn such that each touches the other two, prove that the area included between included between them is equal to $\frac{4}{25}\text{a}^2.$ $\big[\text{Take } \sqrt{3}=1.73\text{ and}\ \pi=3.14\big]$
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