A large conical salt pile is forming in a storage facility. Due to a height-limiting baffle, the pile maintains a fixed height of 12 metres. The base radius of the pile is r r\,r metres and its slant height is l l\,l metres.
Determine an expression for l l\,l in terms of rrr.
The pile is growing such that its base radius is increasing at a constant rate of 1.5 metres per hour.
Find the rate at which the total surface area of the salt pile is changing at the instant the radius is 5 metres. Give your answer in m2\text{m}^2m2 per hour to one decimal place.
[The total surface area, SSS, of a cone is given by S=πr2+πrlS = \pi r^2 + \pi rlS=πr2+πrl]
