Question

The diameter of a circle is equal to the side of the square. What is the area of the square if the area of the circle is 64π sq cm?

A) 128 sq cm B) 196 sq cm C) 108 sq cm D) 256 sq cm

Answer 1

Given :

• The diameter of a circle is equal to the side of the square.
• Area of the circle = 64π cm².

To find :

• Area of square =?

Formula Used :

• Area of circle = πr²
• Area of square = side²

Step-by-step explanation :

It is Given that,

Area of the circle = 64π cm².

As We know that,

Area of circle = πr²

Substituting the values in the above formula, we get,

64π = πr²

r² = 64

r = 8

As it is given that, the diameter of a circle is equal to the side of the square. So,

We know that,

Diameter = 2 × Radius

Substituting the values in the above formula, we get,

= 2 × 8

= 16.

Therefore, Side of the square = 16 cm.

Now,

As We know that,

Area of square = side²

Substituting the values in the above formula, we get,

= (16)²

= 16 × 16

= 256.

Therefore, Area of square = 256 cm².

Hence, Option d). 256 cm² is the correct option.

Answer 2

Answer:

Correct option is : D) 256 sq

Given:

➛The diameter of a circle is equal to the side of the square.

➛The area of the circle is 64π sq cm.

To Find:

The area of the circle.

Solution:

We are given,

➛The diameter of a circle is equal to the side of the square.

➛The area of the circle is 64π sq cm.

➣ Let radius of circle be R.

We know,

◎Area of circle = πR²

by given condition,

◉ Area of the circle is 64π sq cm.

➞ πR² = 64π

➞ R² = 64

➞ R = √64

➞ R = √(8²)

⛬ R = 8 cm

According to given condition,

◎The diameter of a circle is equal to the side of the square.

►Diameter of circle = Side of square

➞ 2 × ( radius ) = Side of square

➞ 2 × ( 8 ) = Side of square

Side of square = 16 cm.

We know ,

►Area of Square = ( Side )²

►Area of Square = ( 16 )²

Area of Square = 256 sq cm.

Hence , correct option is D) 256 sq cm.