The hour hand of a clock is $6\ cm$ long. The area swept by it between $11.20 \ am$ and $11.55\ am$ is:
- A$2.75\ cm^2$
- ✓$5.5\ cm^2$
- C$11\ cm^2$
- D$10\ cm^2$
Answer: B.
View full solution →Question types
Areas Related to Circles question types
277 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
277
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
76 Q→02Assertion (A) & Reason (B) MCQ
5 Q→03Fill In The Blanks[1 Marks ]
20 Q→041 Marks Question
26 Q→052 Marks Questions
59 Q→063 Marks Question
51 Q→075 Marks Questions
35 Q→08Case study (4 Marks)
5 Q→Sample Questions
Areas Related to Circles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the area of a square is same as the area of a circle, then the ratio of their perimeters, in terms of $\pi,$ is:
- A$\pi:\sqrt{3}$
- ✓$2:\sqrt{\pi}$
- C$3:\pi$
- D$\pi:\sqrt{2}$
Answer: B.
View full solution →The radius of a circle is 20cm. It is divided into four parts of equal area by drawing three concentric circles inside it. Then, the radius of the largest of three concentric circles drawn is:
- A$10\sqrt{5}\text{cm}$
- ✓$10\sqrt{3}\text{cm}$
- C$10\sqrt{5}\text{cm}$
- D$10\sqrt{2}\text{cm}$
Answer: B.
View full solution →The area of a circle whose area and circumference are numerically equal, is:
- A$2\pi\text{sq. units}$
- ✓$4\pi\text{sq. units}$
- C$6\pi\text{sq. units}$
- D$8\pi\text{sq. units}$
Answer: B.
View full solution →If the radius of a circle is diminished by 10%, then its area is diminished by:
- A10%
- ✓19%
- C20%
- D36%
Answer: B.
View full solution →Statement-1 (A): The area of a segment of a circle formed by a chord of length 4 cm subtending an angle of $90^{\circ}$ at the centre is $(2 \pi+4) cm ^2$.
Statement-2 (R): The area of a segment of a circle formed by a chord of length 2 a subtending an angle of $90^{\circ}$ at the centre is $(\pi-2) \frac{a^2}{2}$ sq. units.
Statement-2 (R): The area of a segment of a circle formed by a chord of length 2 a subtending an angle of $90^{\circ}$ at the centre is $(\pi-2) \frac{a^2}{2}$ sq. units.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- ✓Statement-1 is False, Statement- 2 is True.
Answer: D.
View full solution →Statement-1 (A): If a race track is in the form of a ring whose outer and inner radii differ by 10 m then the absolute ratio of the area of the track and the sum of the two boundries is $10: 3$.
Statement-2 (R): If a race track is in the form of a ring whose outer and inner radii are $R$ and $r$, then the area of the track and the sum of its two boundries are in the absolute ratio $(R-r): 2$.
Statement-2 (R): If a race track is in the form of a ring whose outer and inner radii are $R$ and $r$, then the area of the track and the sum of its two boundries are in the absolute ratio $(R-r): 2$.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- ✓Statement-1 is False, Statement- 2 is True.
Answer: D.
View full solution →Statement-1 (A): The radius of the circle whose area is equal to the sum of the areas of two circles of radii 10 cm and 24 cm is 26 cm .
Statement-2 (R): The radius rof the circle whose area is equal to the sum of the areas of two circles of radii $r_1$ and $r_2$ is given by $r=r_1{ }^2+r_2{ }^2$.
Statement-2 (R): The radius rof the circle whose area is equal to the sum of the areas of two circles of radii $r_1$ and $r_2$ is given by $r=r_1{ }^2+r_2{ }^2$.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- ✓Statement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement- 2 is True.
Answer: C.
View full solution →Statement-1 (A): The sum of the circumference and ara of a circle of radius 3 cm is in the absolute ratio $5: 8$ to the sum of the circumference and area of a circle of radius 4 cm .
Statement-2 (R): The sums of the circumferences and areas of a two circles of radii $r_1$ and $r_2$ are in the absolute ratio $r_1\left(2+r_1\right): r_2\left(2+r_2\right)$.
Statement-2 (R): The sums of the circumferences and areas of a two circles of radii $r_1$ and $r_2$ are in the absolute ratio $r_1\left(2+r_1\right): r_2\left(2+r_2\right)$.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement- 2 is True.
Answer: A.
View full solution →Statement-1 (A): If the circumferences of two circles are in the raio $4: 5$, then their areas are in the ratio $16: 25$.
Statement-2 (R) : If the circumferences of two circles are in the ratio $C_1: C_2$, then their areas are in the ratio $C_1{ }^2: C_2{ }^2$.
Statement-2 (R) : If the circumferences of two circles are in the ratio $C_1: C_2$, then their areas are in the ratio $C_1{ }^2: C_2{ }^2$.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement- 2 is True.
Answer: A.
View full solution →The number of revolutions made by a circle of radius r to cover a distance s is ____________ .
The area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm $(a>b)$ is ____________ .
View full solution →In Fig. two circles of radii 7 cm each are shown. ABCD is a rectangle and AD and BC are the radii. The area of the shaded region is ____________ .
In Fig. ABCD is a square of side 10 cm and a circle is inscribed in it. The area of the shaded part is ____________ .
The difference in the areas of the regular hexagon circumscribing a circle of radius 10 cm and the regular hexagon inscribed in the circle is ____________ .
If the numerical value of the area of a circle is equal to the numerical value of its circumference, find its radius.
Write the formula for the area of a sector of angle $\theta$ (in degrees) of a circle of radius r.
View full solution →If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?
Find the length of the arc of a circle which subtends an angle of $60^{\circ}$ at the centre of the circle of radius 42 cm.
View full solution →Find the circumference of a circle whose area is $301.84 \ cm^2$.
View full solution →A sector is cut-off from a circle of radius 21cm. The angle of the sector is 120°. Find the length of its arc and the area.
AB is a chord of a circle with centre O and radius 4cm. AB is of length 4cm. Find the area of the sector of the circle formed by chord AB.
The minute hand of a clock is $\sqrt{21}\text{cm}$ long. Find the area described by the minute hand on the face of the clock between 7:00 AM and 7:05 AM.
View full solution →What is the area of a square inscribed in a circle of diameter $p$ cm?
View full solution →Write the formula for the area of a segment in a circle of radius r given that the sector angle is $\theta$ (in degrees).
View full solution →In the following figure, ABCD is a rectangle with AB = 14cm and BC = 7cm. Taking DC, BC and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.
Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions $14cm \times 7cm$. Find the area of the remaining card board.$\Big(\text{Use }\pi=\frac{22}{7}\Big).$
View full solution →The perimeter of a certain sector of a circle of radius 5.6m is 27.2m. Find the area of the sector.
A plot is in the form of a rectangle $A B C D$ having semi-circle on $B C$ as shown in the following figure. If $A B=60 m$ and $B C=28 m$, find the area of the plot.
View full solution →The length of minute hand of a clock is 5cm. Find the area swept by the minute hand during the time period 6:05 AM and 6:40 AM.
A chord of a circle of radius 20cm subtends an angle of 90° at the centre. Find the area of the corresponding major segment of the circle.$(\text{Use }\pi=3.14)$
View full solution →A chord of a circle of radius 14cm makes a right angle at the centre. Find the areas of the minor and major segments of the circle.
A chord PQ of length 12cm subtends an angle of 120° at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.
In the following figure, ABC is a right-angled triangle,$\angle\text{B}=90^\circ,$ AB = 28cm and BC = 21cm. With AC as diameter a semicircle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region correct to two decimal places.
View full solution →A slable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze.
(i) Find the area of the square shaped grass field.
(ii) (a) Find the area of the total field in which these horses can graze.
OR
(b) If the length of the rope of each horse is increased from 7 m to 10 m , find the area grazed by one horse.
(Use $\pi=3.14$ )
(iii) What is area of the field that is left ungrazed, if the length of the rope of each horse is 7 cm ?
View full solution → (i) Find the area of the square shaped grass field.
(ii) (a) Find the area of the total field in which these horses can graze.
OR
(b) If the length of the rope of each horse is increased from 7 m to 10 m , find the area grazed by one horse.
(Use $\pi=3.14$ )
(iii) What is area of the field that is left ungrazed, if the length of the rope of each horse is 7 cm ?
Gorerning council of a local public deoclopment authority of Dehradun decided to build an adrenturous playsround on the top of a hill, which will have adequale space for parking.
After surcey, it was decided to build reclangular playground, with a semi-circular area allotted for parking at one end of the playground. The length and bread th of the reclangular playground are 14 units and 7 units, repectroely. There are two quadrants of radius 2 units on one side for special seats.
(i) What is the total perimeter of the parking area?
(ii) What is the total area of parking and the two quadrants?
(iii) What is the ratio of area of playground to the area of parking arca?
(iv) Find the cost of fencing the playground and parking area at the rate of ₹ 2 per unit.
After surcey, it was decided to build reclangular playground, with a semi-circular area allotted for parking at one end of the playground. The length and bread th of the reclangular playground are 14 units and 7 units, repectroely. There are two quadrants of radius 2 units on one side for special seats.
(i) What is the total perimeter of the parking area?
(ii) What is the total area of parking and the two quadrants?
(iii) What is the ratio of area of playground to the area of parking arca?
(iv) Find the cost of fencing the playground and parking area at the rate of ₹ 2 per unit.
In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made as shown in the figure and its base $A B C D$ is shown from the front side. The rate of silver plating is ₹ $20$ per $cm ^2$. Based on the above, answer the following questions:
(i) What is the area of the quadrant $O D C O$ ?
(ii) Find the area of $\triangle A O B$.
(iii) What is the total cost of silver plating the shaded part $A B C D$ ?
(iv) What is the length of arc $C D$ ?
View full solution →(i) What is the area of the quadrant $O D C O$ ?
(ii) Find the area of $\triangle A O B$.
(iii) What is the total cost of silver plating the shaded part $A B C D$ ?
(iv) What is the length of arc $C D$ ?
A brooch is a small piece of jewellery which has a pin at the back so that it can be fastened on a dress, blouse or coat. Designs of some brooches are shown below.
posisn A: Brooch A is made with silver wire in the form of a circle with diameter 28 mm . The wire is also used for making 4 diameters which divide the circle into 8 equal parts.
Destst B: Brooch B is made of two colours, Gold and Silver. Outer part is made with Gold. The circumference of the silver part is 44 mm and the gold part is 3 mm wide coerywhere.
(i) In design A, the total length of the wire required is
(a) 180 mm $\qquad$ (b) 200 mm $\qquad$ (c) 250 mm $\qquad$ (d) 280 mm
(ii) In design $A$, the area of each sector of the brooch is
(a) $44 mm^2$ $\qquad$ (b) $52 mm^2$ $\qquad$ (c) $77 mm^2$ $\qquad$ (d) $68 mm^2$
(iii) In design B, the circumference of the outer part (golden) is
(a) 48.49 mm $\qquad$ (b) 82.2 mm $\qquad$ (c) 72.50 mm $\qquad$ (d) 62.86 mm
(iv) In design B, the difference of the areas of golden and silver parts is
(a) $18 \pi$ $\qquad$ (b) $44 \pi$ $\qquad$ (c) $51 \pi$ $\qquad$ (d) $64 \pi$
View full solution →posisn A: Brooch A is made with silver wire in the form of a circle with diameter 28 mm . The wire is also used for making 4 diameters which divide the circle into 8 equal parts.
Destst B: Brooch B is made of two colours, Gold and Silver. Outer part is made with Gold. The circumference of the silver part is 44 mm and the gold part is 3 mm wide coerywhere.
(i) In design A, the total length of the wire required is
(a) 180 mm $\qquad$ (b) 200 mm $\qquad$ (c) 250 mm $\qquad$ (d) 280 mm
(ii) In design $A$, the area of each sector of the brooch is
(a) $44 mm^2$ $\qquad$ (b) $52 mm^2$ $\qquad$ (c) $77 mm^2$ $\qquad$ (d) $68 mm^2$
(iii) In design B, the circumference of the outer part (golden) is
(a) 48.49 mm $\qquad$ (b) 82.2 mm $\qquad$ (c) 72.50 mm $\qquad$ (d) 62.86 mm
(iv) In design B, the difference of the areas of golden and silver parts is
(a) $18 \pi$ $\qquad$ (b) $44 \pi$ $\qquad$ (c) $51 \pi$ $\qquad$ (d) $64 \pi$
Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu. During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend whose partner in competition, suggests two design given below:
Design I: This design is made with a circle of radius 32 cm having equilateral triangle $A B C$ in the middle as shown in Fig. 12.11.
Design II: This Pookalam is made with 9 circular designs each of radius 7 cm .
(i) In design-1, the side of equilateral triangle is
(a) $12 \sqrt{3} cm$ $\qquad$ (b) $32 \sqrt{3} cm$ $\qquad$ (c) 48 cm $\qquad$ (d) 64 cm
(ii) In devign-1, the altitude of the equilaleral triangle is
(a) 8 cm $\qquad$ (b) 12 cm $\qquad$ (c) 48 cm $\qquad$ (d) 52 cm
(iii) In design-II, the area of square $A B C D$ is
(a) $1264 cm^2$ $\qquad$ (b) $1764 cm^2$ $\qquad$ (c) $1830 cm^2$ $\qquad$ (d) $1944 cm^2$
(iv) In desgn-II, the area of cach circular region is
(a) $124 cm^2$ $\qquad$ (b) $132 cm^2$ $\qquad$ (c) $144 cm^2$ $\qquad$ (d) $154 cm^2$
View full solution →Design I: This design is made with a circle of radius 32 cm having equilateral triangle $A B C$ in the middle as shown in Fig. 12.11.
Design II: This Pookalam is made with 9 circular designs each of radius 7 cm .
(i) In design-1, the side of equilateral triangle is
(a) $12 \sqrt{3} cm$ $\qquad$ (b) $32 \sqrt{3} cm$ $\qquad$ (c) 48 cm $\qquad$ (d) 64 cm
(ii) In devign-1, the altitude of the equilaleral triangle is
(a) 8 cm $\qquad$ (b) 12 cm $\qquad$ (c) 48 cm $\qquad$ (d) 52 cm
(iii) In design-II, the area of square $A B C D$ is
(a) $1264 cm^2$ $\qquad$ (b) $1764 cm^2$ $\qquad$ (c) $1830 cm^2$ $\qquad$ (d) $1944 cm^2$
(iv) In desgn-II, the area of cach circular region is
(a) $124 cm^2$ $\qquad$ (b) $132 cm^2$ $\qquad$ (c) $144 cm^2$ $\qquad$ (d) $154 cm^2$
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