An industrial conical mold is being manufactured with a fixed vertical height of 12 cm12\text{ cm}12 cm. The mold has a base radius of r cmr\text{ cm}r cm and a slant height of l cml\text{ cm}l cm.
Determine an expression for l in terms of rl\text{ in terms of }rl in terms of r.
During a specific expansion process, the radius of the base is increasing at a constant rate of 1.5 cm per second1.5\text{ cm per second}1.5 cm per second.
Calculate the rate at which the total surface area of the mold is changing at the instant when the radius is 5 cm5\text{ cm}5 cm. Give your answer in cm2 per second\text{cm}^2\text{ per second}cm2 per second correct to one decimal place.
[The total surface area, SSS, of a cone is given by the formula S=πr2+πrlS = \pi r^2 + \pi rlS=πr2+πrl]
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
