A chord of a circle of radius $10\ cm$ subtends a right angle at its centre. The length of the chord $($in $\ cm)$ is :
- A$5\sqrt{2}$
- ✓$10\sqrt{2}$
- C$\frac{5}{\sqrt{2}}$
- D$10\sqrt{3}$
Answer: B.
View full solution →Question types
Areas Related to a Circle question types
325 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
325
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
197 Q→02Assertion (A) & Reason (B) MCQ
43 Q→03True False[1 Marks ]
14 Q→041 Marks Question
49 Q→052 Marks Questions
6 Q→063 Marks Question
5 Q→075 Marks Questions
6 Q→08Case study (4 Marks)
5 Q→Sample Questions
Areas Related to a Circle questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The circumference of a circle is $22\ cm$. The area of its quadrant $($in $cm^2)$ is :
- A$\frac{77}{2}$
- B$\frac{77}{4}$
- ✓$\frac{77}{8}$
- D$\frac{77}{16}$
Answer: C.
View full solution →If the difference between the circumference and the radius of a circle is $37 \ cm,$ then using $\pi = \frac{22}{7},$ the circumference $($in $\ cm)$ of the circle is :
- A$154$
- B$14$
- ✓$44$
- D$7$
Answer: C.
View full solution →If the area of a circle is equal to sum of the areas of two circles of diameters $10\ cm$ and $24\ cm,$ then the diameter of the larger circle $($in $\ cm)$ is :
- A$34$
- ✓$26$
- C$17$
- D$14$
Answer: B.
View full solution →The radii of two circles are $4\ cm$ and $3\ cm$ respectively. The diameter of the circle having area equal to the sum of the areas of the two circles $($in $\ cm)$ is :
- A$5$
- B$7$
- ✓$10$
- D$14$
Answer: C.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$.Mark the correct choice as:
Assertion: The area of the sector of a circle of radius $5\ cm$ is $9.75\ cm^2$ if the corresponding arc length is $ 3.5\ cm.$
Reason: Area of a sector of a circle of radious r and central $\angle\theta$ is $\frac{\theta}{360^\circ}\pi\text{r}^2$
Assertion: The area of the sector of a circle of radius $5\ cm$ is $9.75\ cm^2$ if the corresponding arc length is $ 3.5\ cm.$
Reason: Area of a sector of a circle of radious r and central $\angle\theta$ is $\frac{\theta}{360^\circ}\pi\text{r}^2$
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A).$
- CAssertion $(A)$ is true but reason $(R)$ is false.
- ✓Assertion $(A)$ is false but reason $(R)$ is true.
Answer: D.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R.)$ Mark the correct choice as:
Assertion : If a ball is in the shape of a sphere has a surface area of $221.76\text{ cm}^2$ hen its diameter is $8.4\ cm.$
Reason : If the radius of the sphere be $r,$ then surface area, $\text{S}=4\pi\text{r}^2$ i.e. $\text{r}=\frac{1}{2}\sqrt{\frac{\text{S}}{\pi}}$
Assertion : If a ball is in the shape of a sphere has a surface area of $221.76\text{ cm}^2$ hen its diameter is $8.4\ cm.$
Reason : If the radius of the sphere be $r,$ then surface area, $\text{S}=4\pi\text{r}^2$ i.e. $\text{r}=\frac{1}{2}\sqrt{\frac{\text{S}}{\pi}}$
- ✓Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: A.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : From a solid cylinder, whose height is $12\ cm$ and diameter $10\ cm$ a conical cavity of same height and same diameter is hollowed out.Then, volume of the cone is $\frac{2200}{7}\text{ cm}^3$
Reason : If a conical cavity of same height and same diameter is hollowed out from a cylinder of height h and base radius r, then volume of the cone will be half of the volume of the cylinder.
Assertion : From a solid cylinder, whose height is $12\ cm$ and diameter $10\ cm$ a conical cavity of same height and same diameter is hollowed out.Then, volume of the cone is $\frac{2200}{7}\text{ cm}^3$
Reason : If a conical cavity of same height and same diameter is hollowed out from a cylinder of height h and base radius r, then volume of the cone will be half of the volume of the cylinder.
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- ✓Assertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: C.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$.Mark the correct choice as:
Assertion: The area of the flower bed $($with semi$-$circular ends$)$ shown in figure.
is $(380+50\pi)\text{cm}^2$
Reason: Area of the semi$-$circle is $\frac{\pi\text{r}^2}{2}$ and area of rectangle is length $\times $ breadth.
Assertion: The area of the flower bed $($with semi$-$circular ends$)$ shown in figure.
is $(380+50\pi)\text{cm}^2$
Reason: Area of the semi$-$circle is $\frac{\pi\text{r}^2}{2}$ and area of rectangle is length $\times $ breadth.
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A).$
- CAssertion $(A)$ is true but reason $(R)$ is false.
- ✓Assertion $(A)$ is false but reason $(R)$ is true.
Answer: D.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion : $(A)$ The length of the minute hand of a clock is $7\ cm$.Then the area swept by the minute hand in $5$ minute is $\frac{77}{6}\text{ cm} ^2$
Reason : $(R)$ The length of an arc of a sector of angle $q$ and radius $r$ is given by $\text{l}=\frac{\theta}{360^\circ}\times2\pi\text{r}$
Assertion : $(A)$ The length of the minute hand of a clock is $7\ cm$.Then the area swept by the minute hand in $5$ minute is $\frac{77}{6}\text{ cm} ^2$
Reason : $(R)$ The length of an arc of a sector of angle $q$ and radius $r$ is given by $\text{l}=\frac{\theta}{360^\circ}\times2\pi\text{r}$
- ✓Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: A.
View full solution →Is it true that the distance travelled by a circular wheel of diameter d cm in one nrevolution is $2\pi\text{d cm}?$ Why?
View full solution →The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why?
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false Why?
The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?
In covering a distance s metres, a circular wheel of radius r metres makes $\frac{\text{s}}{2\pi\text{r}}$ revolutions. Is this statement true? Why?
View full solution →Tick the correct answer in the following : Area of a sector of angle $p($in degrees$)$ of a circle with radius $R$ is,
- A$\frac{\text{p}}{180}\times2\pi\text{R}$
- B$\frac{\text{p}}{180}\times2\pi\text{R}^2$
- C$\frac{\text{p}}{360}\times2\pi\text{R}$
- ✓$\frac{\text{p}}{720}\times2\pi\text{R}^2$
Answer: D.
View full solution →Tick the correct answer in the following and justify your choice : If the perimeter and thearea of a circle are numerically equal, then the radius of the circle is :
- ✓$2$ units
- B$\pi\text{ units}$
- C$4$ units
- D$7$ units
Answer: A.
View full solution →If $\pi$is taken as$\frac{22}{7}$, calculate the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution.
View full solution →If the diameter of a semicircular protractor is 14cm, then find its perimeter.
Find the perimeter of Figure 3, where AED$$ is a semi-circle and ABCD is a rectangle.
View full solution →The length of the minute hand of a clock is $14 \ cm$. Find the area swept by the minute hand in $5$ minutes.
View full solution →Area of a sector of angle p (in degrees) of a circle with radius R is
To warm ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80^\circ$ to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (use $ \pi = 3.14 )$
View full solution →A car has two wipers which do not overlap. Each wiper has a blade of length 25cm sweeping through an angle of $115^\circ$. Find the total area cleaned at each sweep of the blades.
View full solution →An umbrella has 8 ribs which are equally spaced (see figure). Assuming umbrella to be a flat circle of radius 45 cm, Find the area between the two consecutive ribs of the umbrella.
A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find:
- the total length of the silver wire required.
- the area of each sector of the brooch.
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A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a $5 \ m$ long rope. Find
View full solution →- the area of that part of the field in which the horse can graze.
- the increase in the grazing area if the rope were $10 \ m$ long instead of 5 m (Use $\pi$ $= 3.14$)
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:
- minor segment
- major sector.
Find the area of a quadrant of a circle whose circumference is 22 cm.
Find the area of a sector of a circle with radius 6 cm, if the angle of the sector is $60^o.$
View full solution →A chord of a circle of radius 12 cm subtends an angle of $120^o$ at the center. Find the area of the corresponding segment of the circle. (Using $\pi$ = 3.14 and $\sqrt3$ = 1.73)
View full solution →A chord of a circle of radius 15 cm subtends an angle of $60^o$ at the center. Find the areas of the corresponding minor and major segments of the circle. (Use $\pi$ = 3.14 and $\sqrt3$ = 1.73)
View full solution →In a circle of radius 21 cm, an arc subtends an angle of $60^o$ at the center. Find:
View full solution →- the length of the arc.
- area of the sector formed by the arc.
- area of the segment formed by the corresponding chord
A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per $cm^2$. (use $\sqrt3$ = 1.7)
View full solution →Find the area of the segment AYB shown in Figure, if the radius of the circle is 21 cm and $\angle$AOB = 120°. (Use $\pi = \frac{22}{7}$).
Sara hold a Japanese folding fan in her hand as shown in the figure. It is shaped like a sector of a circle and made of a thin material such as paper or feather. 'The inner and outer radii are 3cm and 5cm respectively. 'The fan has three colours i.e., red, blue, and green.
Based on the above information, answer the following questions.
- The region given in the figure represents.
- If the region containing red color makes an angle of 20º at the center, then find the perimeter of the region containing red color.
- If the region containing blue color makes an angle of 80º at the center, then find the area of the region having blue color.
Or
If the region containing green color makes an angle of 60º at the center, then find the area of the region having green color.
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 who is a partner in competition, suggests two designs given below.
Design I: This design is made with a circle of radius 32cm leaving equilateral triangle ABC in the middle as shown in the given figure.
Design II: This Pookalam is made with 9 circular design each of radius 7cm.
- The side of equilateral triangle is:
- The altitude of the equilateral triangle is:
- The area of square is:
Or
Area of each circular design is:
Gayatri have a triangular shaped grass field. At the three corners of the field, a cow, a buffalo, and a horse are tied separately to the pegs by means of ropes of 3.5m each to graze in the field, as shown in the figure. Sides of the triangular field are 25m, 24m and 7m. Based on the above information, answer the following questions.
- Area of the region grazed by the cow is ?
- Area of region grazed by the buffalo and the horse is:
- Total area grazed by the cow, the buffalo and the horse is:
Or
Find the area of the field that cannot be grazed.
A builder of residential project have a vacant square land of side 21m. He wants to make a temple in the shape of semi-circle and a park in the shape of two quadrants of a circle as shown in the figure.
Based on the above information, answer the following questions.
- Find the area of square.
- Area of two quadrants, shown in figure, is?
- Find the area of semi-circular temple.
Or
Find the area of unshaded region.
Principle of a school decided to give badges to students who are chosen for the post of Head boy, Head girl, Prefect, and Vice Prefect. Badges are circular in shape with two color area, red and silver, as shown in figure. The diameter of the region representing red color is 22cm and silver color is filled in l0.5 cm wide ring. Based on the above information, answer the following questions.
- The radius of circle representing the red region is:
- Find the area of the red region.
- Find the radius of the circle formed by combining the red and silver region.
Or
Find the area of the silver region.
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