Question : A wire is in the form of square with side 44 cm. It is bent to form a circle. What is the radius of the circle?
Option 1: 28 cm
Option 2: 21 cm
Option 3: 16 cm
Option 4: 32 cm
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Correct Answer: 28 cm
Solution : Side of square, $a$ = 44 cm Let $r$ be the radius. The perimeter of the square = The perimeter of the circle $4 a$ = $2 \pi r$ ⇒ 4 × 44 = 2 × $\frac{22}{7}$ × $r$ ⇒ $r$ = 4 × 7 = 28 Hence, the correct answer is 28 cm.
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Question : When a wire is bent in the form of a square, then the area enclosed by it is 5929 cm2. If the wire is bent into the form of a circle, then what will be the area enclosed by the wire?
Option 1: 7546 cm2
Option 2: 8542 cm2
Option 3: 7632 cm2
Option 4: 6954 cm2
Question : A solid metallic sphere of radius 9 cm is melted and recasted into a wire of radius 2 cm. What is the length of the wire?
Option 1: 343 cm
Option 2: 152 cm
Option 3: 243 cm
Option 4: 184 cm
Question : A solid copper sphere of radius 6 cm is melted and redrawn into a wire, whose radius of cross-section is 8 cm. Find the length of the wire.
Option 1: 9 cm
Option 2: 2.25 cm
Option 3: 4.5 cm
Option 4: 6 cm
Question : The area of a circle is 1386 cm2. What is the radius of the circle? [Use $\pi=\frac{22}{7}$ ]
Option 1: 21 cm
Option 2: 7 cm
Option 3: 14 cm
Option 4: 18 cm
Question : If the circumference of a circle is 13.2 cm, then what is its radius?
Option 1: 1.7 cm
Option 2: 6 cm
Option 3: 21 cm
Option 4: 2.1 cm
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