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
Answers
Answered by
21
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….
Answered by
11
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 .
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 .
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