Discussion
The area of circle increased by 66 sq.cm. If its radius is increased by 1 cm. Find the area of new circle.
Answer: C
The area increases by 66 when the radius goes up by 1, so \(\pi(2r+1)=66\) with \(\pi=22/7\) gives \(2r+1=21\) and \(r=10\). The new radius is 11, and the new area is \(\tfrac{22}{7}\times121=\tfrac{2}{7}\times11^{3}\), option C.
The options with 10, 9 and 12 would come from other radii.
Because \(\pi\times(r+1)^{2}-\pi r^{2}=66\) simplifies to \(2r+1=21\), the radius is 10 cm and the new radius 11 cm. The new area \(\tfrac{22}{7}\times 11^{2}\) can be written as \(\tfrac{2}{7}\times 11^{3}\), which is why option C is printed in that odd form.
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