Maharashtra State BoardSSC (English Medium) 8th Standard

Areas of Some Circles Are Given Below Find Their Diameters. - Mathematics

Advertisements
Advertisements
Sum

Areas of some circles are given below find their diameters.
(1) 176 sq cm
(2) 394.24 sq cm
(3) 12474 sq cm

Advertisements

Solution

(1) 176 sq cm

Ar = πr²

⇒ 176 = `22/7 xx` r²

⇒ r² = `(176 xx 7)/22` = 56

⇒ r = `sqrt[56]`

d = 2r = 2`sqrt[56]`

(2) 394.24 sq cm

Ar = πr²

⇒ 394.24 = `22/7 xx` r²

⇒ `r^2 = 394.24xx7/22`

⇒ `r^2 = (394.24 xx100) /(1xx100)xx (7/22)`

⇒ `r^2 = 39424/100xx7/22`

⇒ `r^2 = 1792/100xx7`

⇒ `r^2 = 12544/100`

⇒ `r^2 = 112^2/10^2`

⇒ r = 11.2

d = 2r = 2 x 11.2 = 22.4 cm

(3) Area of the circle = 12474 sq cm

Ar = πr²

⇒ 12474 = `22/7 xx` r²

⇒ r² = `(12474 xx 7)/22` 

⇒ `r^2 = 567 xx 7`

⇒ r2 = 3969

⇒ r = 63

d = 2r = 2 x 63 = 126 cm

  Is there an error in this question or solution?
Chapter 15: Area - Practice Set 15.6 [Page 104]

APPEARS IN

Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 15 Area
Practice Set 15.6 | Q 2 | Page 104

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.


In Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region [Use `pi=22/7`]


The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distances travelled by their tips in 2 days. (Take π = 22/7)


How many times a wheel of radius 28 cm must rotate to go 352 m? (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)


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


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.


The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram. 

 

 


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, 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.


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.


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.
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.

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


In the given figure, APB and AQO are semicircles and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region.


A chord of a circle of radius 30 cm makes an angle of 60° at the centre of the circle. Find the areas of the minor major segments.


The radii of two concentric circles are 19 cm and 16 cm respectively. The area of the ring enclosed by these circles is


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


Radii of the circles are given below, find their areas.
(1) 28 cm
(2) 10.5 cm
(3) 17.5 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


Find the area and perimeter of the circle with the following :

 Diameter = 77 cm 


Find the circumference of the circle whose area is 25 times the area of the circle with radius 7 cm. 


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. 


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 m2 .


Sand from a cylindrical bucket 32 cm in height and 18 cm in radius is poured onto the ground making a conical heap 24 cm high. Find the radius of the conical heap. 


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 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. 


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 :

Diameter= 6.3 cm 


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 total surface area and volume of a hemisphere whose radius is 10 cm. 


A solid sphere metal is cut through its centre into 2 equal parts. If the diameter of the sphere is 3`1/3` cm , find the total surface of each part, correct to two decimal places. 


Find the diameter of the sphere for the following : 

Surface Area = 221. 76 cm2 


Find the diameter of the sphere for the following : 

Surface Area = `576pi`cm2


The diameter of a circle is 28 cm.
Find its :
(i) Circumference
(ii) Area.


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.


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.


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 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.


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.


The circumferences of two circles are in the ratio 5: 7, find the ratio between their radius.


A circular racing track has inner circumference 528 m and outer circumference 616 m. Find the width of the track.


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`)


A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/sec, calculate the number of complete revolutions the wheel makes in raising the bucket. (Take π =22/7)


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 circles with following: Radius = 2.8cm


Find the area and perimeter of the circles with following: Radius = 10.5cm


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


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


The diameter of a cycle wheel is `4(5)/(11)"cm"`. How many revolutions will it make in moving 6.3km?


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?


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


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


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


Circumference of a circle of diameter 5 cm is ______.


The area of a semicircle of radius 4r is ______.


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


Ratio of circumference of a circle to its radius is always 2π:I.


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.


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×