###### Advertisements

###### Advertisements

A circus tent is cylindrical to a height of 5 m and conical above it. If its diameter is 42 m and slant height of the cone is 53 m, calculate the total area of the canvas required.

###### Advertisements

#### Solution

Height of the cylinder = h = 5 m

Slant height of the cone = I = 53 m

Diameter = 42 m ⇒ radius = r = 21 m

Area of the canvas used = Curved surface area of cylinder + curved surface area of cone

= `2pirh + pirl`

= `(2 xx 22/7 xx 21 xx 5) + (22/7 xx 21 xx 53)`

= 660 + 3498

= 4158 m^{2}

Area of the canvas required = 4158 m^{2}

#### 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.

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

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)

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

21 cm

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`)

An arc of length 15 cm subtends an angle of 45° at the centre of a circle. Find in terms of 𝜋, radius of the circle.

Four equal circles, each of radius 5 cm touch each other as shown in fig. Find the area included etween them.

The perimeter of a rhombus is 60 cm. If one of its diagonal us 18 cm long, find

(i) the length of the other diagonal, and

(ii) the area of the rhombus.

^{°},

^{° }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.

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.**

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}.

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

A wire when bent in the form of an equilateral triangle encloses an area of `121sqrt(3) "cm"^2`. The same wire is bent to form a circle. Find the area enclosed by the circle.

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

The circumference of a circle is equal to the sum of the circumference of two circles having diameters 36 cm and 20 cm. The radius of the new circle is

In making 1000 revolutions, a wheel covers 88 km. The diameter of the wheel 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 area and perimeter of the circle with the following :

Radius= 10.5 cm

Find the area enclosed between two concentric circles, if their radii are 6 cm and 13 cm respectively.

A conical tent requires 264 m^{2} of canvas. If the slant height is 12 m, find the vertical height of the cone.

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

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.

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 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.

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 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 :

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

Find the circumference of the circle whose area is 81π cm ^{2}.

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 .

Find the volume and the surface area of the spheres in the following :

Radius= 2.1 cm

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.

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.

Each wheel of a car is of diameter 80 cm. How many completer revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?

A wheel has a diameter of 84 cm. Find how many completer revolutions must it make to cover 3.168 km.

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 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.

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.

AC and BD are two perpendicular diameter of a circle ABCD. Given that the area of shaded portion is 308 cm^{2} calculate:

(i) The length of AC and

(ii) The circumference of circle

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°.

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.

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.

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 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: Radius = 10.5cm

Find the area and perimeter of the following semicircles: Radius = 1.4cm

Find the area and perimeter of the following semicircles: Diameter = 7cm

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

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.

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.

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 = 70 cm

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

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?

Formula used to find the circumference of a circle is

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

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

Circumference of a circle is always ______.

A wheel of a car covers a distance of 3520 cm in 20 rotations. Find the radius of the wheel?

A circular pond is 17.5 m is of diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per m^{2}.

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 ______.

The distance around a circle is its ______.

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

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.

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.