Question

Find the area of a circle whose circumference is the same as the perimeter of a square of side 11 cm

Answer 1

It is given that circumference of circle =perimeter of square of side 11cm

2pir =4×11cm
2×22/7×r =44cm
44÷7×r = 44cm
r =44×7/44
r = 7cm

Area of circle,
=pir^2
=22/7×7×7
=22/7×49
=22×7
=154cm^2

Answer 2

Answer:

The area of a circle whose circumference is the same as the perimeter of a square of side 11 cm is $153.8cm^{2}$

Step-by-step explanation:

• A square is a polygon with four equal sides

• The perimeter of a square whose side length is (a) is given by the formula

       $P=4a$

• The circumference of a circle is $2\pi r$ and the area of the circle is $\pi r^{2}$, where (r) is the radius of the circle

From the question, it is given that

the side length of the square is $a=11cm$

⇒ the perimeter of the square is $P=4*11=44cm$

the circumference of the circle is the same as the perimeter of the square

⇒$4a=2\pi r$

⇒

$44=2\pi r\\r=44/2\pi =7cm$

now the area of the circle $\pi *7^{2} =153.8cm^{2}$