Question

A circle is inscribed in a square of side 18cm. The ratio of the area of the circle and that of the square is ______.
(A) π : 6
(B) π : 4
(C) 2π : 3
(D) 2π : 5​

Answer 1

Answer:

B

Step-by-step explanation:

Side of the square = 14 m

Side of the square = Diameter of the circle ltbegt ∴Radius of the circle=7m

Area of the circle=π×72=49πm2

Area of the square=142=196m2

Ratio of their areas=49π:196=π:4

Answer 2

Given,

Circle inscribed in a square

Side of the square (s)=18cm

To find,

Area of circle (Ac):Area of square(As)

Solution,

As, circle is inscribed in square,

∴ Circle's diameter (D)= Side of the square (s)

⇒D = 18cm

Using the formula,

Area of circle (Ac)= πr²

∵r=$\frac{D}{2}$

⇒r=$\frac{18}{2}$

⇒r=9cm

On substituting value of r=9,

∴Ac= π(9)²

⇒Ac=81π

Now, Using the formula,

Area of square (As)= s²

⇒As=18²

⇒As=324

Now, Ratio of Ac and As = 81π : 324

⇒Ac:As=π : 4

Hence, Ratio of area of circle and area of square is π : 4. (Option b)