Solution
It is given that the small sphere with radius r has a surface area equal to 45 units square.
The surface area of a sphere with radius r is given by;
[tex]SA=4\pi r^2[/tex]
Since the surface area of the small sphere is 45 units square.
[tex]\begin{gathered} \Rightarrow45=4\pi r^2 \\ \\ \Rightarrow\frac{45}{4\pi}=r^2 \\ \\ \Rightarrow r=\sqrt{\frac{45}{4\pi}} \end{gathered}[/tex]
To find the Surface area with twice the radius, we need to multiply the value of r by 2;
[tex]\Rightarrow R=2r=2\sqrt{\frac{45}{4\pi}}[/tex]
Therefore, the surface area is of a sphere with a radius R is
[tex]\begin{gathered} SA=4\pi R^2 \\ \\ \Rightarrow SA=4\pi(2\sqrt{\frac{45}{4\pi}})^2=4\pi(4\times\frac{45}{4\pi})=4\times45=180\text{ unit}^2 \end{gathered}[/tex]
Hence, the correct option is A.
