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A Steel Wire When Bent is the Form of Square Encloses an Area of 12 Cm2. If the Same Wire is Bent in Form of Circle. Find the Area of Circle. - CBSE Class 10 - Mathematics

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Question

A steel wire when bent is the form of square encloses an area of 12 cm2. If the same wire is bent in form of circle. Find the area of circle.

Solution

Let side of square = s and length of wire be l. As wire is bent into square

l = perimeter of square = 4s.

Area of square = 121cm2 = s2.

S = `sqrt(121)` = 11𝑐𝑚

∴ length of wire l = 4(11) = 44cm

As wire is bent into circle (let radius be r)

Length of wire = circumference

44 = 2𝜋r

`22/7 × 2 × r= 44 ⇒ r = (44×7)/(2×22) = 7`𝑐𝑚
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒 = 𝜋𝑟2

=` 22/7` × 7 × 7

= 22 × 7

= 154𝑐𝑚2

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Solution A Steel Wire When Bent is the Form of Square Encloses an Area of 12 Cm2. If the Same Wire is Bent in Form of Circle. Find the Area of Circle. Concept: Perimeter and Area of a Circle.
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