###### Advertisements

###### Advertisements

A photograph of Billiard/Snooker table has dimensions as `1/10`th of its actual size as shown in the given figure:

The portion excluding six holes each of diameter 0.5 cm needs to be polished at rate of ₹ 200 per m^{2}. Find the cost of polishing.

###### Advertisements

#### Solution

Actual length = 25 × 10 = 250 cm

Actual breadth = 10 × 10 = 100 cm

Area of table = 250 × 100 = 25000 cm^{2}

Radius of 1 hole = `0.5/2` = 0.25 cm

Area of 6 holes = 6 × πr^{2} = `6 xx 22/7 xx 0.25 xx 0.25` = 1.18 cm^{2}

Area of portion excluding holes = 25000 – 1.18 = 24998.8 cm^{2}

∴ Cost of polishing = ₹ `24999/10000 xx 200` = ₹ 500 (approx.)

#### 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. 9, is shown a sector OAP of a circle with centre O, containing ∠θ. AB is perpendicular to the radius OQ and meets OP produced at B. Prove that the perimeter of shaded region is

`r[tantheta+sectheta+(pitheta)/180-1]`

From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take π = 3.14)

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`)

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`)

The minute hand of a clock is √21 𝑐𝑚 long. Find area described by the minute hand on the face of clock between 7 am and 7:05 am

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

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 road which is 7m wide surrounds a circular park whose circumference is 352m. Find the area of road.

Find the area of the rhombus, the length of whose diagonals are 30 cm and 16 cm. Also, find the perimeter of the rhombus.

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

^{° }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.

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}.

The area of a circle is 38.5 cm^{2}. The circumference of the circle 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 = 15 cm , radius = 8 cm

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

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

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

Diameter= 5.6 cm

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 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 .

Find the area and perimeter of the following sector :

Radius= 4.2 cm, angle at the centre is 60 °

Find the area and perimeter of the following sector :

Diameter = 42 cm, angle at the centre is 100·.

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

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.

A cart wheel makes 9 revolutions per second. If the diameter of the wheel is 42 cm, find its speed in km/hr.

A cylindrical beaker of 7 cm diameter is partly filled with water. Determine the number of spherical marbles of diameter 1.4 cm that are to be submerged in it to raise the water level by 5.6 cm

Find the diameter of the sphere for the following :

Surface Area = `576pi`cm^{2}

The diameter of a circle is 28 cm.

Find its :

(i) Circumference

(ii) Area.

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.

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

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`)

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 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.

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.

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.

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

If the perimeter of a semi-circular protractor is 36 cm. Find its diameter.

In the adjoining figure, the radius is 3.5 cm. Find:

(i) The area of the quarter of the circle correct to one decimal place.

(ii) The perimeter of the quarter of the circle correct to one decimal place. ( 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 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: Radius = 10.5cm

Find the area and perimeter of the circles with following: Diameter = 77cm

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

The circumference of a circle is numerically equal to its area. Find the area and circumference of the circle.

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.

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.

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 = 70 cm

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

91 mm

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

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?

Is it true that the distance travelled by a circular wheel of diameter d cm in one revolution is 2 π d cm? Why?

A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle, its radius is ______.

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

Area of circular garden with diameter 8 m is ______.

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

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?

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.