The Solution.
Let the radius of the original circle be r.
By formula,
[tex]\begin{gathered} \text{Area =}\pi r^2 \\ 12.56=3.14r^2 \\ \text{Dividing both sides by 3.14, we get} \\ r^2=\frac{12.56}{3.14}=4 \end{gathered}[/tex]Taking the square root of both sides, we get
[tex]r=\text{ }\sqrt[]{24}\text{ = 2mm}[/tex]For the new circle, the radius is multiplied by 5, that is,
[tex]r=5r=5\times2=10\operatorname{mm}[/tex]So, the area of the new circle is
[tex]\begin{gathered} \text{Area =}\pi r^2=3.14\times10^2 \\ \text{ =3.14}\times100=314mm^2 \end{gathered}[/tex]Hence, the correct answer is 314 square mm.
