1. The diagram below shows a solid circular cone and a solid sphere.

The cone has radius $5x$ cm and height $12x$ cm.
The sphere has radius $r$ cm.
The cone has the same total surface area as the sphere.

Show that  ${r}^{2}=\frac{45}{2}{x}^{2}$.

[The curved surface area, $A$, of a cone with radius $r$ and slant height $l$ is $A= \pi rl$.]
[The surface area, $A$, of a sphere with radius $r$ is $A=4 \pi {r}^{2}$.]