If the perimeter of a square is equal to the radius of a circle whose area is 39424 sq. m. What is the area of the square ?
Options:
A . 441 sq.m
B . 784 sq.m
C . 1225 sq.m
D . Cannot be determined
E . None of these
Answer: Option B Let the radius of the circle be R cm Then, $$\eqalign{ & \pi {R^2} = 39424 \cr & \Rightarrow {R^2} = 39424 \times \frac{7}{{22}} = 12544 \cr & \Rightarrow R = 112\,cm \cr} $$ Perimeter of the square = 112 cm Side of the square : $$\eqalign{ & = \left( {\frac{{112}}{4}} \right)cm \cr & = 28\,cm \cr} $$ ∴ Area of the square : $$\eqalign{ & = \left( {28 \times 28} \right)c{m^2} \cr & = 784\,c{m^2} \cr} $$
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