Question

The area of a circle is 220 cm². The area of ta square inscribed in it is
(a)49 cm²
(b)70 cm²
(c)140 cm²
(d)150 cm²

Answer 1

Answer:

The area of square is 140 cm²

Among the given options option (c) 140 cm² is the correct answer.

Step-by-step explanation:

Given :  

Let the side of a square inscribed in the circle be ‘a’.

Area of a circle , A = 220 cm²

Area of a circle = πr²

220 = πr²

220 = 22/7 × r²

220 × 7 = 22r²

r² = (220 × 7)/22

r² = 10 × 70

r² = 70  

r = √70

Radius of a circle = √70 cm

Diagonal of a square = diameter of a circle

Diagonal of a square  = 2 × radius of a circle

Diagonal of a square  = 2 √70 cm

Diagonal of a square = √2 ×side  

2√70 = √2 × side

side of the square = 2√70/(√2)

Side of the square = 2√70 × √2 / √2×√2

[By rationalising the denominator]

Side of the square = 2√70 × √2 /2

Side of the square = √140

= √(35 × 4)  

= 2√35

Side of the square, a = 2√35 cm

Area of square ,A = side²

A = (2√35)²

A = 4 × 35  

A = 140 cm²

Area of square = 140 cm²

Hence, the area of square is 140 cm²

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Solution:

It is given that square is inscribed in a circle.

Here ,

diameter of a circle = diagonal of a square = d cm

i ) Area of a circle (A) = 220cm² [ given ]

=> (πd²)/4 = 220 cm²

=> (π/2)(d²/2) = 220 cm²

=> [22/(7×2)](d²/2)=220cm²

=> d²/2 = (220 cm² × 2×7)/22

/* Area of the square = d²/2 */

=> Area of the square =

= 10×2×7

= 140 cm²

Therefore,

Option (C) is correct.

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