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) - Mathematics

Advertisements
Advertisements
Sum

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)

Advertisements

Solution

Clearly, minute hand of a clock describes a circle of radius equal to its length i.e., 14 cm.

Since the minute hand rotates through 6º in one minute. Therefore, area swept by the minute hand in one minute is the area of a sector of angle 6º in a circle of radius 14 cm.

Hence, required area A is given by

`A=\frac{\theta }{360}\times \pi r^{2}`

`A={ \frac{6}{360}\times \frac{22}{7}\times (14)^{2}}`

`A={ \frac{1}{60}\times \frac{22}{7}\times 14\times 14}=\frac{154}{15}`

= 10.26 cm2

  Is there an error in this question or solution?

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 Figure , two concentric circles with centre O, have radii 21cm and 42 cm. If ∠ AOB = 60°, find the area of the shaded region. [use π=22/7]


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.


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

21 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`)


Find the angle subtended at the centre of circle of radius 5cm by an arc of length `((5pi)/3)` cm


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 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. 


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. (\[\pi = \frac{22}{7}\]) 


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 - three right angles; find the area of the sector in case.


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.

 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.

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.


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 radius of a circular garden is 100 m. There is a road 10 m wide, running all around it. Find the area of the road and the cost of levelling it at Rs 20 per m2. [Use π = 3.14] 


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.


A wire when bent in the form of a square encloses an area of 484 cm2. If the same wire is bent into the form of a circle, find the area of the circle. 


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. 


A 4.2 m wide road surrounds a circular plot whose circumference is 176 m. Find the cost of paving the road at Rs 75 m 2


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 and perimeter of the following sector :

Radius= 6 cm, angle at the centre is 70° 


Find the area and perimeter of the following sector :

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


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


The wheel of the car makes 10 revolutions per second. If its diameter is 70 cm, find the speed of the car in km per hour. 


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

Radius = 7 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. 


Find the diameter of the sphere for the following : 

Volume = `72pi "cm"^3`


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 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.


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?


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`)


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.


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.


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


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)
_______ _________ 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 circles with following: Diameter = 77cm


Find the circumference of a circle whose area is 81πcm2.


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.


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)


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.


A wire when bent in the form of a square encloses an area of 484cm2. If the same wire is bent into the form of a circle, 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`).


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 = 28 mm


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 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?


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 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?


The perimeter of a sector of radius 5.2 cm is 16.4 cm, the area of the sector is ____________.


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


Circumference of a circle disc is 88 cm. Its radius is ______.


Area of circular garden with diameter 8 m is ______.


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


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.


The moon is about 384000 km from earth and its path around the earth is nearly circular. Find the length of path described by moon in one complete revolution. (Take π = 3.14)


Share
Notifications



      Forgot password?
Use app×