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]
425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.