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) - Mathematics

Advertisements
Advertisements
Sum

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)

Advertisements

Solution

The Circumference of a Circle with diameter d is πd
The Circumference of a Circle with diameter 42cm is π x 42

= `(22)/(7) xx 42`

= 22 x 6
= 132cm
⇒ distance moved in 1 revolution = 132cm
Total distance moved in 9 revolutions 
= 9 x 132cm
= 1188cm
Total distance moved in 1 second = 1188cm
⇒ Total distance moved in 1 hour 
= 1188cm x 60 x 60
= 4276800cm

= `(4276800)/(100 xx 1000)"km"`
⇒ Speed = 42.7km/hr.
∴ Speed = 42.7km/hr.

  Is there an error in this question or solution?
Chapter 24: Perimeter and Area - Exercise 24.3

APPEARS IN

Frank Class 9 Maths ICSE
Chapter 24 Perimeter and Area
Exercise 24.3 | Q 15

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. 2, a circle is inscribed in a ΔABC, such that it touches the sides AB, BC and CA at points D, E and F respectively. If the lengths of sides AB, BC and CA and 12 cm, 8 cm and 10 cm respectively, find the lengths of AD, BE and CF.


A pendulum swings through an angle of 30º and describes an arc 8.8 cm in length. Find the length of the pendulum.


The area of circle, inscribed in equilateral triangle is 154 cms2. Find the perimeter of
triangle.


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. 


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 - 30°  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.


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.
The ratio of circumference and area of a circle is 2:7. Find its circumference.

Choose the correct alternative answer for the following question.

 Find the curved surface area of a cone of radius 7 cm and height 24 cm.

Choose the correct alternative answer for the following question.

 Find the volume of a cube of side 0.01 cm.

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


Find the radius of a circle whose perimeter and area are numerically equal.


The areas of two circles are in the ratio 4: 9. What is the ratio between their circumferences?


In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm,· then find the perimeter of the top of the table.


The wheels of a car make 2500 revolutions in covering a distance of 4.95 km. Find the diameter of a wheel.


The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences 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= 2.8 cm 


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

Height = 16 cm , diameter = 24 cm


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

Diameter= 5.6 cm 


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.


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 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 :

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


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


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 :

Diameter= 6.3 cm 


Find the diameter of the sphere for the following : 

Surface Area = 221. 76 cm2 


The radii of two circles are 25 cm and 18 cm. Find the radius of the circle which has a circumference equal to the sum of circumferences of these two circles. 


The circumference of a given circular park is 55 m. It is surrounded by a path of uniform width of 3.5 m. Find the area of the path.


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 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.


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.


 AC and BD are two perpendicular diameter of a circle ABCD. Given that the area of shaded portion is 308 cm2 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.


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.


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`)


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 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: Radius = 10.5cm


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


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


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


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


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


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 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`).


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


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 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?


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


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?


In covering a distance s metres, a circular wheel of radius r metres makes `s/(2πr)` revolutions. Is this statement true? Why?


Length of tape required to cover the edges of a semicircular disc of radius 10 cm is ______.


The area of a square is 100 cm2. The circumference (in cm) of the largest circle cut of it is ______.


Ratio of the circumference of a circle to its diameter is denoted by symbol ______.


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


Ishika has designed a small oval race track for her remote control car. Her design is shown in the given figure. What is the total distance around the track? Round your answer to the nearest whole centimetre.


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.


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 m2. Find the cost of polishing.


Share
Notifications



      Forgot password?
Use app×