# SPM Additional Mathematics 2019, Paper 2 (Question 7)

Quesion 7:
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 $A=2\pi \left(\frac{18}{r}+\frac{{r}^{2}}{3}\right).$

(a)(i)
The solid expands when heated. It is given that the surface area of the solid changes at the
rate of 1.4π cm2s-1. Find the rate of change of its radius in, cm s-1, when its radius is 6 cm.

(ii) Find the approximate change in the surface area of the solid, in terms of π, when its radius
increases from 6 cm to 6.02 cm.
[6 marks]

(b) If a solid of a same shape is to be formed in such that the total surface area is minimum, find
the minimum total surface area of the solid, in terms of π. [4 marks]

Solution:
(a)(i)

(a)(ii)

(b)