###### Advertisements

###### Advertisements

The radii of two circles are 19 cm and 9 cm, Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

###### Advertisements

#### Solution

Let the radius of the required circle be r.

Now, Circumference of the required circle = Circumference of circle having radius 19 cm + Circumference of circle having radius 9 cm

⇒ 2πr = 2π × 19 + 2π × 9

⇒ r = 19 + 9

⇒ r = 28 cm

Hence, the radius of the required circle is 28 cm.

#### APPEARS IN

#### RELATED QUESTIONS

The radius of a circle is 7 cm. find the circumference of the circle.

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 PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region. [Use π=3.14]

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

A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the costs of the rope, if it cost ₹ 4 per meter (Take `pi = 22/7`)

The circumference of two circles are in ratio 2:3. Find the ratio of their areas

The side of a square is 10 cm. find the area of circumscribed and inscribed circles.

The hypotenuse of a right-angled triangle is 65 cm and its base is 60 cm. Find the length of perpendicular and the area of the triangle.

The shape of the cross section of a canal is a trapezium. If the canal is 10 m wide at the top, 6 m wide at the bottom and the area of its cross section is `640m^2` , find the depth of the canal.

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

^{°},

In the given figure, if A(P-ABC) = 154 cm^{2 }radius of the circle is 14 cm, find

(1) `∠APC`

(2) l ( arc ABC) .

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.

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.

^{°}and its length is 44 cm, find the circumference of the circle.

Choose the correct alternative answer for the following question.

**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.

**Choose the correct alternative answer for the following question.**

^{3}.

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

Four equal circles are described about the four corners of a square so that each touches two of the others, as shown in the figure. Find the area of the shaded region, if each side of the square measures 14 cm.

The radii of two concentric circles are 19 cm and 16 cm respectively. The area of the ring enclosed by these circles is

In making 1000 revolutions, a wheel covers 88 km. The diameter of the wheel is

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is

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

Height = 12 cm , radius = 5 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

A bucket is raised from a well by means of a rope wound round a wheel of diameter 35 cm. If the bucket ascends in 2 minutes with a uniform speed of 1.1 m per sec, calculate the number of complete revolutions the wheel makes in raising the bucket.

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

Find the area enclosed between two concentric circles, if their radii are 6 cm and 13 cm respectively.

The area between the circumferences of two concentric circles is 2464 cm^{2}. If the inner circle has circumference of 132 cm, calculate the radius of outer circle.

A wire bent in the form of an equilateral triangle has an area of 121 `sqrt 3` cm^{2}. If the same wire is bent into the form of a circle , find the area enclosed by the wire.

The circumference of a circle is equal to the perimeter of a square. The area of the square is 484 sq. m. Find the area of the circle.

Find the area and perimeter of the following semi-circle :

Diameter= 7 cm

A 7 m road surrounds a circular garden whose area is 5544 m^{2}. Find the area of the road and the cost of tarring it at the rate of Rs.150 per sq m.

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 lawn is in the shape of a semi-circle of diameter 42 m. The lawn is surrounded by a flower bed of width 7 m all around. Find the area of the flower bed in m^{2} .

Find the area of a circular field that has a circumference of 396 m.

The base circumferences of two cones are the same. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surface areas.

The diameter of a right circular cylinder is 12 m and the slant height is 10 m. Find its curved surface area and the total surface area .

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

Radius= 2.1 cm

Find the diameter of the sphere for the following :

Volume = `72pi "cm"^3`

The radii of two circles are 48 cm and 13 cm. Find the area of the circle which has its circumference equal to the difference of the circumferences of the given two circles.

An express train is running between two stations with a uniform speed. If the diameter of each wheel of the train is 42 cm and each wheel makes 1200 revolutions per minute, find the speed of the train.

A wheel has a diameter of 84 cm. Find how many completer revolutions must it make to cover 3.168 km.

There are two circular gardens A and B. The circumference of garden A is 1.760 km and the area of garden B is 25 times the area of garden A. Find the circumference of garden B.

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 diameter of a circular field is 56 m. Find its circumference and cost of fencing it at the rate of ₹80 per m. (Take π =`22/7`)

The radius of two circles are 20 cm and 13 cm. Find the difference between their circumferences. (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 radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radius 15 cm and 8 cm.

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.

A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/sec, calculate the number of complete revolutions the wheel makes in raising the bucket. (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) |

_______ | _________ | 616 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.

Find the circumference of a circle whose area is 81πcm^{2}.

Find the radius and area of the circle which has circumference equal to the sum of circumferences of the two circles of radii 3 cm and 4 cm respectively.

The circumference o a garden roller is 280cm. How many revolutions does it make in moving 490m?

The area between the circumference of two concentric circles is 2464cm^{2}. If the inner circle has a circumference of 132cm, calculate the radius of the outer circle.

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

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 m^{2}. Find the cost of ploughing the field.

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 = 28 mm

Find the circumference of the circles whose radii are given below.

49 cm

Find the circumference of the circles whose radii are given below.

91 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

A Rose garden is in the form of circle of radius 63 m. The gardener wants to fence it at the rate of ₹ 150 per metre. Find the cost of fencing?

In the formula, C = 2πr, ‘r’ refers to

Circumference of a circle is always ______.

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 numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?

Circumference of a circle disc is 88 cm. Its radius is ______.

Length of tape required to cover the edges of a semicircular disc of radius 10 cm is ______.

Area of circular garden with diameter 8 m is ______.

The circumference of a circle whose area is 81 πr^{2}, is ______.

Circumference ‘C’ of a circle can be found by multiplying diameter ‘d’ with ______.

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.

Find the total cost of wooden fencing around a circular garden of diameter 28 m, if 1 m of fencing costs ₹ 300.