if you want to remove an article from website contact us from top.

# if the perimeter of a square is equal to the perimeter of a circle, then the ratio of their areas is

Category :

### Mohammed

Guys, does anyone know the answer?

get if the perimeter of a square is equal to the perimeter of a circle, then the ratio of their areas is from screen.

## If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

Click here👆to get an answer to your question ✍️ If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

Question

A

B

C

D

## 11:14

Medium Open in App Solution Verified by Toppr

Correct option is B)

Step -1: Equate perimeter of a square and circle.

Let r be the radius of a circle

and be the side of a square.

From the given data,

Perimeter of a square = Circumference of a circle

⇒4a=2πr ⇒ r a ​ = 2 π ​ …(1)

Step -2: Calculate the ratio of area of square and circle.

Area of circle:Area of square

⇒ Area of square Area of circle ​ = a 2 πr 2 ​ ⇒ Area of square Area of circle ​ =π( a r ​ ) 2 ⇒ Area of square Area of circle ​ =π( π 2 ​ ) 2 (From equation (1)) ⇒ Area of square Area of circle ​ =π π 2 4 ​ ⇒ Area of square Area of circle ​ = π 4 ​ ⇒ Area of square Area of circle ​ = 22 4×7 ​ (∵π= 7 22 ​ ) ⇒ Area of square Area of circle ​ = 11 14 ​

Hence, option (B) 14:11 is correct answer.

1752 524

स्रोत : www.toppr.com

## If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is a 4 : π b π : 4 c π : 7 d 7 : π

If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is a 4 : π b π : 4 c π : 7 d 7 : π

Byju's Answer Standard X Mathematics Area of a Circle If the perime... Question

If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is

(a) 4 : π (b) π : 4 (c) π : 7 (d) 7 : π Open in App Solution

Circumference = perimeter

2 π r = 4 a r = 2 a π Area of the square Area of circle = a 2 π r 2 = a 2 π × 2 a π × 2 a π = π a 2 4 a 2 = π 4 = π : 4 Suggest Corrections 37

SIMILAR QUESTIONS

Q. If the perimeter of a square is equal to the circumference of a circle, then the ratio of their areas

π π whenπ=227 is. (a) 14 : 11 (b) 11 : 14 (c) 22 : 7 (d) 7 : 22

Q. If the area of a square is same as the area of a circle, then the ratio of their perimeters, in terms of π, is

(a) π : 3 (b) 2 : π π π (c) 3 : π π π (d) π π π:2

Q. A circle is inscribed in a square of side 14 m. The ratio of the area of the circle and that of

the square is (a) π : 3 (b) π : 4 (c) π : 2 (d) π : 1

Q. The area of a square is equal to the area of a circle. The ratio between the side of the square

and the radius of the circle is

(a) π : 1 (b) 1 : π (c) 1 : π (d) π : 1

Q. If the circumference of a circle is equal to the perimeter of a square then the ratio their areas is:

(a) 22 : 7 (b) 14 :11 (c) 7 :22 (d) 7 :11 View More RELATED VIDEOS

Introduction MATHEMATICS Watch in App EXPLORE MORE Area of a Circle

Standard X Mathematics

स्रोत : byjus.com

## If the perimeter of a circle is equal to that of a square then find the ratio of their areas

If the perimeter of a circle is equal to that of a square then find the ratio of their areas - Given: The perimeter of a circle is equal to that of a square.To do: To find the ratio of their areas.Solution:As given the perimeter of the circle is equal to that of the square.\$P_{circle}=P_{square}\$Let \$r\$ be the radius of the circle & \$a\$ be the side of square, then\$2pi r=4a\$\$frac{r}{a}=frac

## If the perimeter of a circle is equal to that of a square, then find the ratio of their areas.

Given: The perimeter of a circle is equal to that of a square.To do: To find the ratio of their areas.Solution:

As given the perimeter of the circle is equal to that of the square.

P circle = P square Pcircle=Psquare Let r r

be the radius of the circle &

a a

be the side of square, then

2πr=4a 2πr=4a r a = 4 2π = 2 π ra=42π=2π Now, Area of the circle Area of the square = π r 2 a 2

Area of the circleArea of the square=πr2a2

⇒ Area of the circle Area of the square = π× 2 2 π 2

⇒Area of the circleArea of the square=π×22π2

= 4 π =4π

Hence the ratio of Area of a circle to that of a square is

4 π 4π . Tutorialspoint

Simply Easy Learning

Updated on 10-Oct-2022 10:43:40

4K+ Views

Print Article

Related Articles

If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.

If the circumference of a circle and the perimeter of a square are equal, then find relationship between radius of the circle and side of the square.

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

If the perimeter and the area of a circle are numerically equal, then find the radius of the circle.

From a point ( P ), two tangents ( P A ) and ( P B ) are drawn to a circle with centre ( O ). If ( O P= ) diameter of the circle, show that ( Delta A P B ) is equilateral.

From an external point ( P ), tangents ( P A ) and ( P B ) are drawn to a circle with centre ( O ). At one point ( E ) on the circle tangent is drawn, which intersects ( P A ) and ( P B ) at ( C ) and ( D ) respectively. If ( P A=14 mathrm{~cm} ), find the perimeter of ( triangle P C D ).

The perimeter of a rectangle is equal to that of a square with side 12m. If the length of the rectangle is 10m. Find its breadth.

If a point A(0,2) A(0,2)

is equidistant from the points

B(3,p) B(3,p) and C(p,5) C(p,5)

, then find the value of

p p .

If p is a prime number and q is a positive integer such that

p+q=1696 p+q=1696

. If p and q are co prime numbers and their LCM is 21879, then find p and q.

In triangleABC triangleABC , P P divides the side AB AB such that AP:PB=1:2 AP:PB=1:2 . Q Q is a point in AC AC such that PQparallelBC PQparallelBC

. Find the ratio of the areas of ( Delta A P Q ) and trapezium BPQC.

In the below figure, ( A B C D ) is a square of side ( 2 a ). Find the ratio between the areas of the incircle and the circum-circle of the square."\n

In the figure, ( P A ) and ( P B ) are tangents to the circle from an external point ( P ). ( C D ) is another tangent touching the circle at ( Q ). If ( PA=12 cm, QC=QD=3 cm, ) then find ( P C+P D )."\n

A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio

8:5 8:5

, show that the radius of each is to the height of each as

3:4 3:4 .

If the distance between the points

(4,p) (4,p) and (1,0) (1,0)

is 5, then find the value of

p p . Previous Page Next Page Advertisements

स्रोत : www.tutorialspoint.com

Do you want to see answer or more ?
Mohammed 13 day ago

Guys, does anyone know the answer?