If the circumference of a circle is equal to the perimeter of square, then which one of the following is correct

This question was previously asked in
HTET TGT Mathematics 2018 Official Paper
View all HTET Papers >
  1. Area of circle = Area of square
  2. Area of circle > Area of square
  3. Area of circle < Area of square
  4. None of the above

Answer (Detailed Solution Below)

Option 2 : Area of circle > Area of square
Free
HTET PGT Official Computer Science Paper - 2019
4.4 K Users
60 Questions 60 Marks 60 Mins

Detailed Solution

Download Solution PDF

Formula used:

1. Area of circle = πr2

2. Circumference of circle = 2πr

3. Perimeter of square = 4a

4. Area of square = a2

Where, 

r = radius of circle and 

a = side of the square 

Calculation:

Let the radius of the circle is r and the side of the square is a.

Then the area of a circle

A= πr= 3.14 r2       ------(1)

According to the question, 

Circumference of a circle = perimeter of the square

⇒ 2πr = 4a

⇒ a = πr/2  

Hence the area of square

 \(a^2\ =\ (\frac{π r}{2})^2\) 

\(\Rightarrow \ a^2\ =\ 2.46\ r^2\)        -----(2)

From the equation (1) and (2), we can say that, Area of circle > Area of the square.

Latest HTET Updates

Last updated on Jun 6, 2025

-> The HTET TGT Applciation Portal will reopen on 1st June 2025 and close on 5th June 2025.

-> HTET Exam Date is out. HTET TGT Exam will be conducted on 26th and 27th July 2025

-> Candidates with a bachelor's degree and B.Ed. or equivalent qualification can apply for this recruitment.

-> The validity duration of certificates pertaining to passing Haryana TET has been extended for a lifetime.

-> Enhance your exam preparation with the HTET Previous Year Papers.

More Circles Questions

Get Free Access Now
Hot Links: online teen patti real money teen patti master download mpl teen patti teen patti 3a teen patti master apk best