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A wire when bent in the form of a square encloses an area of $992.25 cm 2$ . If the same wire is bent in the form of a semicircle, what will be the radius of the semicircle so formed?

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24.5

45.2

42.2

45.5

answer is A.

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Detailed Solution

We need to find the radius of the semicircle obtained. It is given that the wire used to create the semicircle was bent in the form of a square with an area

992.25 cm 2

A r e a = a 2

We know that the given area is

992.25 cm 2

.Hence,

a 2 = 992.25

a = 992.25 = 31.5 cm

Let us find the perimeter of the square,

Perimeter = 4a

Perimeter = 4 × 31.5 = 126 cm

It is given that the same wire is used to form a semicircle. Hence,

Perimeter of the square = circumference of the semicircle…(i)

We know that the circumference of a semicircle with radius r is given as

Circumference = πr+2r

Let us substitute this in (i). We will get

π r + 2 r = 126

r (π + 2) = 126

r (227 + 2) = 126

r 367 = 126

r = 126 × 736

r = 24.5 cm

Hence, the radius of the semicircle is 24.5 cm.

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