###### Advertisements

###### Advertisements

A wire is in the form of a circle of radius 42 cm. It is bent into a square.

Determine the side of the square and compare the area of the regions enclosed in two cases.

###### Advertisements

#### Solution

Radius of the circle= 42 cm

Area of the cirde = π r^{2 }

`= 22/7 xx 42 xx 42`

= 5544 cm^{2}

Area of the cirde = 5544 cm^{2}

Circumference of the circle = 2 π r

`= 2 xx 22/7 xx 42`

= 264 cm

Perimeter of the square = Circumference of the circle = 264 cm

4 x side = 264

side = `264/4` = 66 cm

Side of square =66 cm

Area of square = side^{2} = 66 x 66 = 4356 cm^{2}

Area of a circle : Area of square = `5544/4356 = 14/11`

Side of square = 66 cm

Area of the cirde: Area of square = 14 : 11

#### APPEARS IN

#### 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.

Find the area of the sector of a circle whose radius is 14 cm and angle of sector is 45º

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region

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

28 mm

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`)

Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)

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

The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour. (Take π = 3.14)

A doorway is decorated as shown in the figure. There are four semi-circles. BC, the diameter of the larger semi-circle is of length 84 cm. Centres of the three equal semicircles lie on BC. ABC is an isosceles triangle with AB = AC. If BO = OC, find the area of the shaded region. (Take `pi = 22/7`)

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

A plot is in the form of rectangle ABCD having semi-circle on BC. If AB = 60m and BC = 28m, find the area of plot.

Find the area of a right – angled triangle, the radius of whose, circumference measures 8 cm and the altitude drawn to the hypotenuse measures 6 cm.

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.

^{°},

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 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.

^{°}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.

**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.

Find the perimeter of a semicircular protractor whose diameter is 14 cm.

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 wheels of the locomotive of a train are 2.1 m in radius. They make 75 revolutions in one minute.

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.

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.

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

Height = 8 cm , diameter = 12 cm

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 when bent in the form of a square encloses an area of 484 cm^{2}. If the same wire is bent into the form of a circle, find the area of the circle.

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.

A conical tent with a capacity of 600 m^{3} stands on a circular base of area 160 m^{2} Find in m^{2} the area of the canvas.

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

Diameter= 5.6 cm

A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.

Sand from a cylindrical bucket 32 cm in height and 18 cm in radius is poured onto the ground making a conical heap 24 cm high. Find the radius of the conical heap.

A horse is tied with a 21 m laig rope to the corner of a field which is in the shape of an equilateral triangle. Find the area of the field over which it can graze.

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

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.

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 :

Diameter= 6.3 cm

Find the total surface area and volume of a hemisphere whose radius is 10 cm.

A solid sphere metal is cut through its centre into 2 equal parts. If the diameter of the sphere is 3`1/3` cm , find the total surface of each part, correct to two decimal places.

The cost of fencing a circular field at the rate of ₹ 240 per meter is ₹ 52,800. The field is to be ploughed at the rate of ₹ 12.50 per m^{2}. Find the cost of pouching the field.

In the given figure, the area of the shaded portion is 770 cm^{2}. If the circumference of the outer circle is 132 cm, find the width of the shaded portion.

The shaded portion of the figure, given alongside, shows two concentric circles. If the circumference of the two circles is 396 cm and 374 cm, find the area of the shaded portion.

The circumference of a given circular park is 55 m. It is surrounded by a path of uniform width of 3.5 m. Find the area of the path.

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

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

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 center O of a circle of a radius 1.3 cm is at a distance of 3.8 cm from a given straight line AB. Draw a circle to touch the given straight line AB at a point P so that OP = 4.7 cm and to touch the given circle externally.

Find the area of a circle whose circumference is 22 cm.

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 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 of a circular field that has a circumference of 396m.

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

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

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

A cart wheel makes 9 revolutions per second. If the diameter of the wheel is 42cm, find its speed in km per hour. (Answer correct to the nearest km)

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.

Sudhanshu divides a circular disc of radius 7 cm in two equal parts. What is the perimeter of each semicircular shape disc? (Use π = `22/7`)

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

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

49 cm

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 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?

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

Circumference of a circle is always ______.

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?

The area of a quadrant of a circle whose circumference is 22 cm, is ____________.

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

The distance around a circle is its ______.

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

The moon is about 384000 km from earth and its path around the earth is nearly circular. Find the length of path described by moon in one complete revolution. (Take π = 3.14)