Please answer this.

Dear Student,
The ratio of the image size (magnification) to object size is 1/2
So,
$$\begin{gathered} Magnitifcation=\frac{image size}{object size}=\frac{image dis\tan ce \left(v\right)}{object dis\tan ce \left(u\right)} \\ So, \\ \frac{v}{u}=\frac{1}{2}\Rightarrow u=2v \end{gathered}$$
Given,
Diameter of the Christmas tree ball be D = 9.0 cm
Radius of the tree ball will be R = D/2 = 4.5 cm
Focal length of the convex mirror formed:
$$\begin{gathered} f=\frac{R}{2}=\frac{4.5}{2}=2.25cm \\ Now, \\ From mirror formula: \\ \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ v and u will be on the opposite side of the mirror so, \\ \frac{1}{v}+\frac{1}{-u}=\frac{1}{f} \\ \frac{2}{u}-\frac{1}{u}=\frac{2}{4.5}=\frac{4}{9} \\ \frac{1}{u}=\frac{4}{9} \\ u=\frac{9}{4}=2.25cm=2.3 cm \end{gathered}$$

Regards