examday

/TMUA

A tank is a right circular cone with its vertex at the bottom. Its vertical height is $10\,\mathrm{cm}$ and its top radius is $6\,\mathrm{cm}$. Initially it contains some water.

Water is added at a constant volume per minute. In one time interval, the depth of the water increases by $2\,\mathrm{cm}$. In the next time interval of the same duration, it increases by $1\,\mathrm{cm}$. The tank does not overflow.

What is the depth of the water, in centimetres, at the end of the first of these two intervals?

The volume of a cone of radius $r$ and height $h$ is $\frac13\pi r^2h$.