Discussion

Explanation:

A quarter circle can be considered as a sector with θ = 90° as shown below.

Hence, the area of the quarter circle has to be equal to the area of the sector and the perimeter has to be the same as the perimeter of the sector. 

Area of sector O-ACB = 1/4 × area of circle = 1/4 × πr² = 1/4 × 22/7 × 14 × 14 = 154 cm²

Perimeter of sector O-ACB = length(arc ACB) + length(OA) + length(OB) 

= $\left[\frac{1}{4}\times 2\mathrm{\pi r}\right]$ + r + r = $\left[\frac{1}{4}\times 2\times \frac{22}{7}\times 14\right]$ + 14 + 14 = 50 cm.

Hence, option (a).

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