Question

If a wire is bent into the shape of a square, then the area of the square is 81 cm² . When wire is bent into a semi-circular shape, then the area of the semi-circle will be

(a) 22 cm²

(b) 44 cm²

(c) 77 cm²

(d) 154 cm²

Answer 1

We have given that a wire is bent in the form of square of side a cm such that the area of the square is . If we bent the same wire in the form of a semicircle with radius r cm, the perimeter of the wire will not change.

perimeter of the square = perimeter of semi circle

………(1)

We know that area of the square = .

Now we will substitute the value of a in the equation (1),

Now we will substitute.

Multiplying both sides of the equation by 7 we get,

Now we will divide both sides of the equation by 36 we get, r = 7

Therefore, radius of the semi circle is 7cm.

Now we will find the area of the semicircle.

Area of the semicircle

Therefore, area of the semicircle is .

Hence the correct answer is option (c).