SPM 2019 Add Maths Paper 2, Question 7Differentiation

A metal solid is formed by combining a cone and a cylinder with common radius, r cm. The total surface area of the solid, A cm², is given by A = 2pi(18/r + r²/3). (a)(i) The solid expands when heated. It is given that the surface area of the solid changes at the rate of 1.4*pi cm² s⁻¹. Find the rate of change of its radius, in cm s⁻¹, when its radius is 6 cm. (a)(ii) Find the approximate change in the surface area of the solid, in terms of pi, when its radius increases from 6 cm to 6.02 cm. (b) If a solid of the same shape is to be formed such that the total surface area is minimum, find the minimum total surface area of the solid, in terms of pi.