A steel wire is bent in the form of a square of area 121 cm2. If the same wire is bent to form a circle, find the area of the circle. (Assume π=227)
11 cm2
44 cm2
121 cm2
154 cm2
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A steel wire is bent in the form of a square of area 121 cm2. If the same wire is bent to form a circle, find the area of the circle. (Assume π=227)
11 cm2
44 cm2
121 cm2
154 cm2
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Answer:
Area of squared wire =121cm
2
⇒s×s=121
⇒ side of square =11cm
Perimeter of square =4×s
=4×11=44cm=Circumference of circular wire
⇒2π×r=44
⇒r=
2π
44
⇒r=7cm
Now, Area of Circular wire =π×r
2
=
7
22
×7×7
=154cm
2
So, area of the wire when bent in circular shape is 154cm
2.
[tex]\huge\sf\red{Answer:}[/tex]
⇒ Option - (D) 154 cm²
Step-by-step explanation:
Given:
⇒ A steel wire is bent in the form of a square of area 121 cm². If the same wire is bent to form a circle.
Find:
⇒ Find the area of the circle.
Note:
⇒ [tex]\sf \pi= \dfrac{22}{7}[/tex]
Calculations:
⇒ According to the question, we know that 121² is the area of squared wire. Side × Side = 121², Side of a square = 11 cm.
Using formula:
⇒ Perimeter of square: [tex]\sf 4 \times Side[/tex]
Calculations:
⇒ [tex]\sf 4 \times 11 = 44[/tex]
⇒ [tex]\sf 2 \pi \times r = 44[/tex]
⇒ [tex]\sf r = \dfrac{44}{2 \pi}[/tex]
⇒ [tex]{\sf{\underline{\boxed{\green{\sf{7 \: cm }}}}}}[/tex]
Now, finding the area of the circle:
⇒ [tex]\sf \pi \times r^2[/tex]
⇒ [tex]\sf \dfrac{22}{7} \times 7 \times 7[/tex]
⇒ [tex]{\sf{\underline{\boxed{\green{\sf{154 \: cm^2 }}}}}}[/tex]
Therefore, 154 cm² is the area of the circle.