###### Advertisements

###### Advertisements

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?

###### Advertisements

#### Solution

Radius of the circular garden, r = 56 m

Circumference of the circular garden, c = 2πr

= `2xx22/7xx56`

= 352 m

∴ Length of the wire needed for one round of fencing = c = 352 m

Cost of one round of fencing = length of wire × cost per metre

= 352 × 40

= 14080 rupees

Cost of four round of fencing = 4 × 14080 = 56320 rupees

#### 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 Figure , two concentric circles with centre O, have radii 21cm and 42 cm. If ∠ AOB = 60°, find the area of the shaded region. [use π=22/7]

The length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in one minute. (Use π = 22/7)

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`)

Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take `pi = 22/7`)

How many times a wheel of radius 28 cm must rotate to go 352 m? (Take `pi = 22/7`)

The minute hand of clock is10cm long. Find the area of the face of the clock described by the minute hand between 8am and 8:25 am

In circle of radius 6cm, chord of length 10 cm makes an angle of 110° at the centre of circle find Length of arc

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

^{°},

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. (\[\pi = \frac{22}{7}\])

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) .

^{° }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 area of a minor sector of a circle is 3.85 cm^{2 }and 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.

^{°}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.

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.

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

Find the radius of a circle whose perimeter and area are numerically equal.

Find the area of the sector of a circle having radius 6 cm and of angle 30°. [Take π = 3.14]

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm ⨯ 7 cm. Find the area of the remaining cardboard.

The side of a square is 10 cm. Find the area of the circumscribed circle. [π = 3.14]

The radius of the wheel of a vehicle is 42 cm. How many revolutions will it complete in a 19.8-km-long journey?

In the given figure, ABCD is a trapezium of area 24.5 cm^{2} , If AD || BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region.

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 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.

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

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

Radius= 1.4 cm

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

Diameter= 7 cm

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

Diameter= 5.6 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.

The sum of diameter of two circles is 112 cm and the sum of their areas is 5236 cm^{2} Find the radii of the two circles.

The sum of the radii of two circles is 10.5 cm and the difference of their circumferences is 13. 2 cm. Find the radii of the two circles.

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 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.

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 .

A cylindrical bucket, whose base radius is 20 cm, is filled with water to a height of 25 cm. A heavy iron spherical ball of radius 10 cm is dropped to submerge completely in water in the bucket. Find the increase in the level of water.

Find the diameter of the sphere for the following :

Surface Area = 221. 76 cm^{2}

A metal wire, when bent in the form of an equilateral triangle of largest area, encloses an area of 484 `sqrt3` cm^{2}. If the same wire is bent into the form of a circle of largest area, find the area of this circle.

The radii of two circles are 25 cm and 18 cm. Find the radius of the circle which has a circumference equal to the sum of circumferences of these two circles.

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 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 radius of two circles are in the ratio 3 : 5, find the ratio between their circumferences.

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.

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 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: Diameter = 5.6cm

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.

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 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.

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 = 56 m

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

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

A wire of length 1320 cm is made into circular frames of radius 7 cm each. How many frames can be made?

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?

Formula used to find the circumference of a circle is

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 area of a semicircle of radius 4r is ______.

The distance around a circle is its ______.

Ratio of the circumference of a circle to its diameter is denoted by symbol ______.

Circumference ‘C’ of a circle is equal to 2π × ______.

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

A dinner plate is in the form of circle. A circular region encloses a beautiful design as shown in the given figure. The inner circumference is 352 mm and outer is 396 mm. Find the width of circular design.