In the Given Figure, O is the Centre of the Sector. ∠ Roq = ∠ Mon = 60° . Or = 7 Cm, and Om = 21 Cm. Find the Lengths of Arc Rxq and Arc Myn. ( π = 22 7 ) - Geometry Mathematics 2

Advertisements
Advertisements
Sum

In the given figure, O is the centre of the sector. \[\angle\]ROQ =  \[\angle\]MON = 60° . OR = 7 cm, and   OM = 21 cm. Find the lengths of  arc RXQ and arc MYN. (\[\pi = \frac{22}{7}\]) 

Advertisements

Solution

Given: ∠ROQ = ∠MON = 60°,

radius (r) = OR = 7 cm, radius (R) = OM = 21 cm 

To find: Lengths of arc RXQ and arc MYN.

i. Length of arc RXQ = `θ/360 xx 2π"r"`

`= 60/360 × 2 × 22/7 × 7`

`= 1/6 × 2 × 22`

= 7.33 cm

ii. Length of arc MYN = `θ/360 xx 2π"R"`

`= 60/360 × 2 × 22/7 × 21`

`= 1/6 × 2 × 22 × 3`

= 22 cm

∴ The lengths of arc RXQ and arc MYN are 7.33 cm and 22 cm respectively.

  Is there an error in this question or solution?
Chapter 7: Mensuration - Practice set 7.3 [Page 155]

APPEARS IN

Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 7 Mensuration
Practice set 7.3 | Q 8 | Page 155

RELATED QUESTIONS

In figure, ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and side AC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from A to the circle.


In Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region [Use `pi=22/7`]


The circumference of a circle exceeds the diameter by 16.8 cm. Find the radius of the circle.


Find the circumference of the circle with the following radius (Take `pi = 22/7`) 

14 cm


Find the circumference of the circle with the following radius (Take `pi = 22/7`) 

28 mm


ABC is an isosceles right-angled triangle with ∠ABC = 90°. A semi-circle is drawn with AC as the diameter. If AB = BC = 7 cm, find the area of the shaded region. [Take π = 22/7]


The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram. 

 

 


Find the area of trapezium whose parallel sides are 11 m and 25 m long, and the nonparallel sides are 15 m and 13 m long. 

 


Find the circumferences of a circle whose radius is 7 cm.


In the given figure, the radius of the circle is 7 cm and m ( arc MBN) = 60°,
find  A(O - MCN). 

The radius of a sector of a circle is 7 cm. If the measure of the arc of the sector is - 30°  find the area of the sector in case.

The radius of a sector of a circle is 7 cm. If the measure of the arc of the sector is 210°,  find the area of the sector in case.


The radius of a sector of a circle is 7 cm. If the measure of the arc of the sector is - three right angles; find the area of the sector in case.


The area of a minor sector of a circle is 3.85 cmand the measure of its central angle is 36°. Find the radius of the circle.


In the given figure,

\[\square\] PQRS is a rectangle. If PQ = 14 cm, QR = 21 cm, find the areas of the parts x, y, and z.  


Choose the correct alternative answer for the following question.
The ratio of circumference and area of a circle is 2:7. Find its circumference.

Choose the correct alternative answer for the following question.
If measure of an arc of a circle is 160° and its length is 44 cm, find the circumference of the circle.
 

Choose the correct alternative answer for the following question.

The curved surface area of a cylinder is 440 cm 2 and its radius is 5 cm. Find its height.


Choose the correct alternative answer for the following question.

A cone was melted and cast into a cylinder of the same radius as that of the base of the cone. If the height of the cylinder is 5 cm, find the height of the cone.

 

Choose the correct alternative answer for the following question.

 Find the volume of a cube of side 0.01 cm.

Diagonal of a square is 20 cm. Find the length and perimeter of the square.


What is the perimeter of a square which circumscribes a circle of radius a cm?


Find the length of the arc of a circle of diameter 42 cm which subtends an angle of 60° at the centre.


A sector of 56°, cut out from a circle, contains 17.6 cm2. Find the radius of the circle.


Find the area of a quadrant of a circle whose circumference is 88 cm.


The diameter of a wheel is 84 cm. How many revolutions will it make to cover 792 m?


Radii of the circles are given below, find their areas.
(1) 28 cm
(2) 10.5 cm
(3) 17.5 cm


Areas of some circles are given below find their diameters.
(1) 176 sq cm
(2) 394.24 sq cm
(3) 12474 sq cm


Diameter of the circular garden is 42 m. There is a 3.5 m wide road around the garden. Find the area of the road.


Find the area of the circle if its circumfence is 88 cm.


Find the area and perimeter of the circle with the following:

Diameter= 35 cm 


Find the curved surface area , the total surface area and the volume of a cone if its : 

Height = 16 cm , diameter = 24 cm


The area of a circular ring enclosed between two concentric circles is 88 cm 2. Find the radii of the two circles, if their difference is 1 cm.


The area between the circumferences of two concentric circles is 2464 cm2. If the inner circle has circumference of 132 cm, calculate the radius of outer circle.


A conical tent with a capacity of 600 m3 stands on a circular base of area 160 m2 Find in m2 the area of the canvas. 


A canvas tent is in the shape of a cylinder surmounted by a conical roof. The common diameter of the cone and the cylinder is 14 m. The height of the cylindrical part is 8 m and the height of the conical roof is 4 m. Find the area of the canvas used to make the tent. 


A circus tent is cylindrical to a height of 5 m and conical above it. If its diameter is 42 m and slant height of the cone is 53 m, calculate the total area of the canvas required. 


Find the area grazed by a horse tied with a 11. 2 m rope to a corner of a field measuring 25m by 15 m.


Find the circumference of the circle whose area is 81π cm 2


The diameter of a wheel is 1.4m. How many revolutions does it make in moving a distance of 2.2 kms?


The wheel of the car makes 10 revolutions per second. If its diameter is 70 cm, find the speed of the car in km per hour. 


The speed of the car is 66 km/hour. If each wheel of the car is 140 cm in diameter, find the number of revolutions made by each wheel per minute.


Find the volume and the surface area of the spheres in the following :

Radius= 2.1 cm 


Find the volume and the surface area of the spheres in the following :

Radius = 7 cm 


Find the diameter of the sphere for the following : 

Volume = `523 17/21` cm3


Find the diameter of the sphere for the following : 

Volume = `72pi "cm"^3`


The circumference of a circular field is 308 m. Find is:
(i) Radius
(ii) Area.


The sum of the circumference and diameter of a circle is 116 cm. Find its radius. 


In the given figure, the area of the shaded portion is 770 cm2. If the circumference of the outer circle is 132 cm, find the width of the shaded portion.


Each wheel of a car is of diameter 80 cm. How many completer revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?


Draw the circumcircle of Δ PMT in which PM = 5.4, P = 60°, M = 70°.


The radius of a circle is 21 cm. Find the circumference (Take π = `3 1/7`).


The circumference of a circle is 440 cm. Find its radius and diameter. (Take π = `22/7`)


The perimeter of a square and the circumference of a circle are equal. If the length of each side of the square is 22 cm, find:
(i) perimeter of the square.
(ii) circumference of the circle.
(iii) radius of the circle.


Find the diameter of a circle whose circumference is equal to the sum of circumference of circles with radius 10 cm, 12 cm, and 18 cm.


The circumference of a circle is eigth time the circumference of the circle with a radius of 12 cm. Find its diameter.


The circumferences of two circles are in the ratio 5: 7, find the ratio between their radius.


Each side of a square is 44 cm. Find its perimeter. If this perimeter is equal to the circumference of a circle, find the radius of the circle.


The circumference of a circle exceeds its diameter by 18 cm. find the radius of the circle.


A circular racing track has inner circumference 528 m and outer circumference 616 m. Find the width of the track.


The inner circumference of a circular track is 264 m and the width of the track is 7 m. Find:
(i) the radius of the inner track.
(ii) the radius of the outer circumference.
(iii) the length of the outer circumference.
(iv) the cost of fencing the outer circumference at the rate of ₹50 per m.


If the perimeter of a semi-circular protractor is 36 cm. Find its diameter.


In the adjoining figure, the radius is 3.5 cm. Find:
(i) The area of the quarter of the circle correct to one decimal place.
(ii) The perimeter of the quarter of the circle correct to one decimal place. ( Take π = `22/7`)


Complete the table below.

Radius (r)  Diameter (d) Circumference (c)
7 cm ______ _______

Complete the table below.

Radius (r)  Diameter (d) Circumference (c)
_______ 28 cm _________

Complete the table below.

Radius (r)  Diameter (d) Circumference (c)
_______ _________ 72.6 cm

If the circumference of a circle is 176 cm, find its radius.


The radius of a circular garden is 56 m. What would it cost to put a 4-round fence around this garden at a rate of 40 rupees per metre?


The wheel of a bullock cart has a diameter of 1.4 m. How many rotations will the wheel complete as the cart travels 1.1 km?


The diameter of a circle is 5.6 cm. Find its circumference.


The diameter of the wheel of a cart is 1.05 m. How much distance will the cart cover in 1000 rotations of the wheel?


Find the area and perimeter of the circles with following: Diameter = 35cm


Find the area and perimeter of the following semicircles: Radius = 1.4cm


The diameter of a cycle wheel is `4(5)/(11)"cm"`. How many revolutions will it make in moving 6.3km?


Find the circumference of the circle whose area is 25times the area of the circle with radius 7cm.


A 4.2m wide road surrounds a circular plot whose circumference is 176m. Find the cost of paving the road at Rs.75per m2.


The cost of fencing a circular field at the rate of Rs.250 per metre is Rs.55000. The field is to be ploughing at the rate of Rs.15 per m2. Find the cost of ploughing the field.


What is the circumference of a circle of diameter 10 cm (Take π = 3.14)?


The radius of a circular plot is 7.7 metres. How much will it cost to fence the plot with 3 rounds of wire at the rate of 50 rupees per metre?


The radius of the wheel of a bus is 0.7 m. How many rotations will a wheel complete while traveling a distance of 22 km?


Diameters of different circles are given below. Find their circumference (Take π = `22/7`)

d = 70 cm


Diameters of different circles are given below. Find their circumference (Take π = `22/7`)

d = 28 mm


The diameter of a circular well is 4.2 m. What is its circumference?


The diameter of the bullock cart wheel is 1.4 m. Find the distance covered by it in 150 rotations?


A ground is in the form of a circle whose diameter is 350 m. An athlete makes 4 revolutions. Find the distance covered by the athlete


If the circumference of a circle is 82π, then the value of ‘r’ is


Circumference of a circle is always ______.


A wheel of a car covers a distance of 3520 cm in 20 rotations. Find the radius of the wheel?


The cost of fencing a circular race course at the rate of ₹ 8 per metre is ₹ 2112. Find the diameter of the race course


The cost of decorating the circumference of a circular lawn of a house at the rate of ₹ 55 per metre is ₹ 16940. What is the radius of the lawn?


In reference to a circle the value of π is equal to ______.


Area of circular garden with diameter 8 m is ______.


Ratio of circumference of a circle to its radius is always 2π:I.


A circle with radius 16 cm is cut into four equal parts and rearranged to form another shape as shown in the below figure:


Does the perimeter change? If it does change, by how much does it increase or decrease?


Ishika has designed a small oval race track for her remote control car. Her design is shown in the given figure. What is the total distance around the track? Round your answer to the nearest whole centimetre.


A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also find area of the path.


A photograph of Billiard/Snooker table has dimensions as `1/10`th of its actual size as shown in the given figure:


The portion excluding six holes each of diameter 0.5 cm needs to be polished at rate of ₹ 200 per m2. Find the cost of polishing.


Share
Notifications



      Forgot password?
Use app×