Question

a square of side 3cm is circumscribed by a circle. then the area of the circle is

Answer 1

Given:

A square of side 3cm is circumscribed by a circle.

To find:

The area of the circle.

Solution:

Side length of square = 3 cm

Length of diagonal is

$Diagonal=\sqrt{2}\times side$

$Diagonal=\sqrt{2}\times 3$

$Diagonal=3\sqrt{2}\ cm$

Square is circumscribed by a circle, so diameter of circle is equal to length of diagonal.

$Diameter=3\sqrt{2}\ cm$

Radius is half of diameter.

$Radius=\dfrac{3\sqrt{2}}{2}\ cm$

Area of a circle is

$Area=\pi r^2$

where, r is radius.

Substitute $r=\dfrac{3\sqrt{2}}{2}$ in the above formula.

$Area=\pi (\dfrac{3\sqrt{2}}{2})^2$

$Area=\dfrac{22}{7}\times \dfrac{9\times 2}{4}$   $[\because \pi=\dfrac{22}{7}]$

$Area=\dfrac{22}{7}\times 4.5$

$Area=14.142857$

$Area\approx 14.14$

Therefore, the area of the circle is 14.14 sq. cm.

Answer 2

Answer:

14.14 sq cm

Step-by-step explanation:

4.5 cm²

14.14 sq