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

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

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Question

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

**A**

## 22:7

**B**

## 14:11

**C**

## 7:22

**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.

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## 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

## 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.

AcademicMathematicsNCERTClass 10

**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

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