A solid sphere of radius 7 cm is sliced into two equal halves by a single cut through its centre. By how many ${\text{cm}}^2$ does the total exposed surface area increase? Take π = 22/7.

The curved skin is untouched; the cut simply exposes two new flat circles of radius 7 cm, one on each half. Increase = 2π$r^2=2\times (22/7)\times 49=308{\text{cm}}^2.(154{\text{cm}}^2$ counts only one of the two new faces; $924{\text{cm}}^2$ is the new total surface, $2\times 3$π$r^2$, not the increase; $616{\text{cm}}^2$ is the sphere's original surface.)