The radius of a circle whose area is numerically 110 more than its circumference is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7 units
For a circle of radius \(r\), the area is \(\pi r^2\) and the circumference is \(2\pi r\). The question says the area is 110 more than the circumference, which gives one equation in \(r\).
\(\pi r^2=2\pi r+110\)
\(\pi r(r-2)=110\)
\(\displaystyle r(r-2)=110\times\frac{7}{22}=35\)
\(35=7\times5\), so \(r=7\)