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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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## [Solved] If the perimeter of a circle and a square are equal, then wh

Given: The perimeter of the circle is equal to that of the square. Formula: If “r” is the radius of the circle and a” is the sid

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## Question

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## If the perimeter of a circle and a square are equal, then what is the ratio of the area of the circle to that of the square?

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1 ∶ π 2 ∶ π 3 ∶ π 4 ∶ π

## Answer (Detailed Solution Below)

Option 4 : 4 ∶ π

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## Detailed Solution

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**Given:**

The perimeter of the circle is equal to that of the square.

**Formula:**

If “r” is the radius of the circle and a” is the side of the square,

1) Perimeter of a circle = 2πr

2) Area of a circle = πr2

3) Perimeter of a square = 4a

4) Area of a square = a2

**Calculation:**

Let “r” be the radius of the circle and “a” be the side of the square,

According to the question,

The perimeter of the circle is equal to that of the square.

2πr = 4a

⇒ r/a = 4/(2π) = 2/π ----(1)

Now, the ratio of the area of circle and Area of square:

⇒ πr2/a2 ----(2)

From equation (1) and (2),

πr2/a2 = π(2/π)2 ⇒ πr2/a2 = 4/π

**∴ The ratio of the area of a circle to that of a square is 4 ∶ π.**

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

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

Advertisement Remove all ads MCQ Fill in the Blanks

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

### OPTIONS

13 : 22 14 : 11 22 : 13 11 : 14 Advertisement Remove all ads

### SOLUTION

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is **14 : 11**.

**Explanation:**

Let radius of circle be r and side of a square be a.

Perimeter of a circle = Perimeter of a square

∴ 2πr=4a ⇒ a=πr2 .....(i) Now, Area of circle Area of square

Area of circleArea of square=πr2(a)2=π2(πr2)2

......[From equation (i)]

= πr2π2r24=4π = 4227=2822 = 1411

Concept: Area of Circle

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Chapter 13: Areas Related to Circles - Exercise 13.6 [Page 73]

Q 39 Q 38 Q 40

### APPEARS IN

RD Sharma Class 10 Maths

Chapter 13 Areas Related to Circles

Exercise 13.6 | Q 39 | Page 73

NCERT Mathematics Exemplar Class 10

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