If a given stick of length 628 m is bent in the form a circle and later bent into a square. Which of them, circle or square will have greater area? [4 MARKS]

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Solution

Formula: 1 Mark
Steps: 2 Marks
Result: 1 Mark

Length of the stick is equal to the perimeter of circle and square individually.
Circle of given radius has a perimeter of 628 m.
Side of square = 157 m
Radius of the given circle:
= $\frac{628}{2 \times π}$
= 100m

Area of the circle:
= $π$ $\times$ $r^{2}$
= $π$ $\times$ $100^{2}$
= $3.14 \times$ $100^{2}$
= $31400 m^{2}$

Area of the square
= $length \times length$
= $157 \times 157$
= $24649 m^{2}$

The area of circle is greater than area of square.

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