###### Advertisements

###### Advertisements

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

###### Advertisements

#### Solution

Circumference = 176 cm

Circumference = 2πr ..........(where 'r' is the radius of circle)

176 = `2xx22/7xx"r"`

176 × 7 = 2 × 22 × r

1232 = 44r

`1232/44` = r

r = 28

∴ The radius of the circle = 28 cm

#### 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.

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]

An elastic belt is placed around the rim of a pulley of radius 5 cm. (Fig. 10) From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley. Also find the shaded area (use *π* = 3.14 and `sqrt3=1.73)`

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

A bicycle whell makes 5000 revolutions in moving 11 km. Find the diameter of the wheel

The minute hand of a clock is 10cm long. Find the area of the face of the clock described by the minute hand between 9 A.M. and 9.35 A.M.

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

28 mm

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

21 cm

A steel wire when bent is the form of square encloses an area of 12 cm2. If the same wire is bent in form of circle. Find the area of circle.

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

A car travels 1 km distance in which each wheel makes 450 complete revolutions. Find the radius of wheel.

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) .

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 cm^{2 }and the measure of its central angle is 36^{°}. Find the radius of the circle.

^{°}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.

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

A chord of a circle of radius 30 cm makes an angle of 60° at the centre of the circle. Find the areas of the minor major segments.

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 = 16 cm , diameter = 24 cm

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

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.

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.

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

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 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.

A 4.2 m wide road surrounds a circular plot whose circumference is 176 m. Find the cost of paving the road at Rs 75 m ^{2}.

Two circles touch each other externally. The sum of their areas is 5811 cm^{2} and the distance between their centres is 10 cm. Find the radii of the two circles.

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} .

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.

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 area and perimeter of the following sector :

Radius= 6 cm, angle at the centre is 70°

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

Find the diameter of the sphere for the following :

Volume = `72pi "cm"^3`

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

The radius of a circle is 5 m. Find the circumference of the circle whose area is 49 times the area of the given circle.

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.

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.

The diameters of the front and the rear wheels of a tractor are 63 cm and 1.54 m respectively. The rear wheel is rotating at `24 6/11` revolutions per minute. Find:

(i) the revolutions per minute made by the front wheel.

(ii) the distance traveled bu the tractor in 40 minutes.

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

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.

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 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.

Using a ruler and compasses only:

(i) Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ∠ ABC = 120°.

(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.

(iii) Measure ∠ BCP.

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 |

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

The circumference of a circle exceeds its diameter by 450 cm. Find the area of the circle.

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

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

A wire in the form of a circle of radius 42cm. It is bent into a square. Determine the side of the square and compare the area of the regions enclosed in the two cases.

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 = 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

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

91 mm

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?

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 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?

Circumference of a circle of diameter 5 cm 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 ______.

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

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.

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the midpoints of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.

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)