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

Answer:

The area of semicircle is  77 cm².

Among the given options option (c) 77 cm² is the correct answer.

Step-by-step explanation:

Given :  

Area of a square = 81 cm²

Area of a square = side²

side² = 81 cm²

Side = √81

Side = 9 cm

Side of a square ,a = 9 cm  

Perimeter of a square ,P = 4a

P = 4 × 9  

P = 36 cm

Perimeter of a square = 36 cm

Perimeter of a  square  = Circumference of the semicircle

[Same wire is bent , so perimeter of both the shapes will be same]

36 = πr + 2r

36 = 22/7 × r +  2r

36 = 22r/7 + 2r

36 = (22r + 14r)/7

36 × 7  = 36r

r = (36 × 7)/36

r = 7 cm

Radius of a circle = 7 cm

Area of semicircle,A = ½ πr²

A = ½ × 22/7 × 7 × 7

A = 11× 7

A = 77 cm²

Area of semicircle = 77 cm²

Hence, the area of semicircle is  77 cm².

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Area of square = 81 cm²= a²
length of one side = a = 9
length of wire = perimeter of square = 4a
4×9= 36
circumference of semi circle = 2r+πr=36
r(2+22/7)=36
r(36/7)=36
r=7
Area of semi circle πr²/2
11/7×49
11×7
77 cm²
hence the option c is the correct answer .