A Conical Tent with a Capacity of 600 M3 Stands on a Circular Base of Area 160 M2 Find in M2 the Area of the Canvas. - Mathematics

Advertisements
Advertisements
Sum

A conical tent with a capacity of 600 m3 stands on a circular base of area 160 m2 Find in m2 the area of the canvas. 

Advertisements

Solution

Area of the circular base = 160m2 

`pir^2 = 160`

⇒ `r = sqrt((160 xx 7)/22)`

⇒ `r = sqrt(50.909)` = 7.134 m

Therefore , radius = 7.134 m

Capacity or Volume of the tent = 600m3

`1/3pir^2h = 600`

⇒ `1/3 xx 22/7 xx 7.13 xx 7.13 xx h = 600`

⇒ `h = (600 xx 3 xx 7)/(7.13 xx 7.13 xx 22)`

⇒ h = 11.265m

Therefore , vertical height = 11.265 m

We know slant height (l) = 

l = `sqrt(r^2 + h^2)`

⇒ `l = sqrt(7.134^2 + 11.265^2)`

⇒ `l = sqrt(177.624) = 13.327`

Therefore , slant height = 13.327 m

The curved surface area = `pirl = 22/7 xx 7.134 xx 13.327` = 298.9m2

Hence , the area of the canvas = 298.9 m2

  Is there an error in this question or solution?
Chapter 20: Mensuration II - Exercise 20.1

APPEARS IN

Frank ICSE Class 10 Mathematics Part 2
Chapter 20 Mensuration II
Exercise 20.1 | Q 3

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

The radius of a circle is 7 cm. find the circumference 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)


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

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


A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the costs of the rope, if it cost ₹ 4 per meter (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)


Find the circumference of a circle whose area is 301.84 cm2.


A playground has the shape of rectangle, with two semicircles on its smaller sides as diameters, added to its outside. If the sides of rectangle are 36m and 24.5m. find the area of playground.


The hypotenuse of a right-angled triangle is 65 cm and its base is 60 cm. Find the length of perpendicular and the area of the triangle. 


The parallel sides of trapezium are 12 cm and 9cm and the distance between them is 8 cm. Find the area of the trapezium.


Find the circumferences of a circle whose radius is 7 cm.


In the given figure, the radius of the circle is 7 cm and m ( arc MBN) = 60°,
find  A(O - MCN). 

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 cm2  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 210°,  find the area of the sector in case.


The area of a minor sector of a circle is 3.85 cmand 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.  


Choose the correct alternative answer for the following question.
If measure of an arc of a circle is 160° 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.

 Find the volume of a cube of side 0.01 cm.

Choose the correct alternative answer for the following question.

Find the side of a cube of volume 1 m3.

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


A sector of 56°, cut out from a circle, contains 17.6 cm2. Find the radius of the circle.


In the given figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.


The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.


OACB is a quadrant of a circle with centre O and its radius is 3.5 cm. If OD = 2 cm. find the area of

  1. quadrant OACB 
  2. the shaded region.


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:

Diameter= 35 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? 


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 cm2. If the inner circle has circumference of 132 cm, calculate the radius of outer circle.


A wire bent in the form of an equilateral triangle has an area of 121 `sqrt 3` cm2. If the same wire is bent into the form of a circle , find the area enclosed by the wire.


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. 


Two circles touch each other externally. The sum of their areas is 5811 cm2 and the distance between their centres is 10 cm. Find the radii of the two circles.


A canvas tent is in the shape of a cylinder surmounted by a conical roof. The common diameter of the cone and the cylinder is 14 m. The height of the cylindrical part is 8 m and the height of the conical roof is 4 m. Find the area of the canvas used to make the tent. 


The sum of diameter of two circles is 112 cm and the sum of their areas is 5236 cm2 Find the radii of the two circles. 


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 :

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


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


Find the circumference of the circle whose area is 81π cm 2


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 :

Radius = 7 cm 


Find the diameter of the sphere for the following : 

Volume = `72pi "cm"^3`


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.


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 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 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`)


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 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.


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.


In the adjoining figure, the crescent is formed by two circles which touch at the point A. O is the centre of bigger circle. If CB = 9 cm and DE = 5 cm, find the area of the shaded portion.


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?


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


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


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


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 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.


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 m2. Find the cost of ploughing the field.


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


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?


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


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?


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


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?


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


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


Circumference of a circle of diameter 5 cm is ______.


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


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 m2. Find the cost of polishing.


Share
Notifications



      Forgot password?
Use app×