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]
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.