Mirror Equation and Focal Length

Wrap a rubber ball of diameter $12 \mathrm{cm}$ completely with an aluminium foil and make the surfaces smooth. Where will be the image of an object kept $12 \mathrm{cm}$ away from the centre of the ball? Is the image real or virtual?

A shaving mirror of focal length $72 \mathrm{cm}$ is kept in a beauty clinic. A man uses it standing $18 \mathrm{cm}$ away from the mirror. At what distance will the image be formed? Is the image real or virtual? What is the magnification of the image?

A motorcyclist observes a car coming from behind with a magnification $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.$. If the actual distance between the car and the bike is $30 \mathrm{m}$ calculate the radius of curvature of the mirror.

Imagine that a spherical mirror gives a $5$ times magnified and inverted image. The distance between the object and image is $5 \mathrm{m}$. If so determine whether the mirror is concave or convex. How much will be the focal length of the mirror?