Question : A piece of wire, when bent to form a circle, will have a radius of 84 cm. If the wire is bent to form a square, the length of one side of the square is:
Option 1: 152 cm
Option 2: 132 cm
Option 3: 168 cm
Option 4: 225 cm
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Correct Answer: 132 cm
Solution : Given: A piece of wire, when bent to form a circle, will have a radius of 84 cm. Length of the wire = circumference of the circle = $2\pi r$ ⇒ $2×\frac{22}{7}×84=528$ So, the perimeter of the square = 528 cm ⇒ One side of the square = $\frac{528}{4}=132$ cm Hence, the correct answer is 132 cm.
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Question : A wire is in the form of a square with a side of 11 cm. It is bent to form a circle. What is the radius of the circle?
Option 1: 11 cm
Option 2: 5 cm
Option 3: 9 cm
Option 4: 7 cm
Question : A piece of wire 132 cm long is bent successively in the shapes of an equilateral triangle, a square, and a circle. The area will be largest in the shape of:
Option 1: Circle
Option 2: Equilateral triangle
Option 3: Square
Option 4: Equal in all the shapes
Question : A solid copper sphere of radius 9 cm is hammered and moulded into a wire of radius 2 cm. What is the length of this wire?
Option 1: 224 cm
Option 2: 183 cm
Option 3: 198 cm
Option 4: 243 cm
Question : In a circle, a 14 cm long chord is 24 cm from the centre of the circle. Find the length of the radius of the circle.
Option 1: 30 cm
Option 2: 25 cm
Option 3: 50 cm
Option 4: 27 cm
Question : The circumference of a circle is equal to the perimeter of an equilateral triangle. If the radius of the circle is 7 cm, what is the length of the side of the equilateral triangle?
Option 1: $\frac{22}{3}$ cm
Option 2: $\frac{44}{3}$ cm
Option 3: $44$ cm
Option 4: $22$ cm
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