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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions 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), matched to the AQA A Level Maths (7357) 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.
