###### Advertisements

###### Advertisements

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

###### Advertisements

#### Solution

Let the radius of a circle = r cm

⇒ Circumference of a circle = 2πr cm

Diameter of a circle = 2r cm

Now, Circumference of a circle - Diameter of a circle = 450m

⇒ 2πr - 2r = 450

⇒ 2r(π - 1) = 450

⇒ `2"r"(22/7 - 1)` = 450

⇒ `2"r" xx (15)/(7)` = 450

⇒ r = `(450 xx 7)/(2 xx 15)`

= 105cm

∴ Area of a circle

= πr^{2}

= `(22)/(7) xx 105 xx 105`

= 34650cm^{2}.

#### 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 Fig. 7, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and radius OP while arc PBQ is a semi-circle drawn on PQ ad diameter with centre M. If OP = PQ = 10 cm show that area of shaded region is `25(sqrt3-pi/6)cm^2`.

If the perimeter of a semi-circular protractor is 66 cm, find the diameter of the protractor (Take π = 22/7).

A race track is in the form of a ring whose inner circumference is 352 m, and the outer circumference is 396 m. Find the width of the track.

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

14 cm

If the circumference of a circular sheet is 154 m, find its radius. Also find the area of

the sheet. (Take `pi = 22/7`)

Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹ 15. ( Take π = 3.14)

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)

Below fig shows a sector of a circle, centre O. containing an angle 𝜃°. Prove that

Area of shaded region is`r^2/2(tantheta −(pitheta)/180)`

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.

^{°},

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.

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.

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

The area of a circle inscribed in an equilateral triangle is 154 cm^{2}. Find the perimeter of the triangle.

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

Three equal circles, each of radius 6 cm, touch one another as shown in the figure. Find the area of enclosed between them.

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

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

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.

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

Height = 8 cm , diameter = 12 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.

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

Radius= 1.4 cm

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.

Find the area enclosed between two concentric cirdes of radii 6.3 cm and 8.4 cm. A third concentric circle is drawn outside the 8.4 cm circle, so that the area enclosed between it and 8.4 cm cirde is the same as that between two inner circles. Find the radii of the third circle correct to two decimal places .

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.

Find the diameter of the sphere for the following :

Surface Area = `576pi`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 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.

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.

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 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 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 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.

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.

Construct an angle PQR = 45°. Mark a point S on QR such that QS = 4.5 cm. Construct a circle to touch PQ at Q and also to pass through S.

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

Construct the circumcircle of the ABC when BC = 6 cm, B = 55° and C = 70°.

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.

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.

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?

The sum of the circumference and diameter of a circle is 176 cm. Find the area of the circle.

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.

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

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

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.

Find the perimeter of the given shape (Take π = `22/7`).

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 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?

Formula used to find the circumference of a circle is

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

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

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

The distance around a circle is its ______.

**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?

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