Edexcel Mathematics June 2022 · Paper 1 · Question 15 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

June 2022 · Paper 1 · Question 15 · 10 marks

15. A h D r B 0.8 rad r E C F Figure 5 A company makes toys for children. Figure 5 shows the design for a solid toy that looks like a piece of cheese. The toy is modelled so that • face ABC is a sector of a circle with radius r cm and centre A • angle BAC = 0.8 radians • faces ABC and DEF are congruent • edges AD, CF and BE are perpendicular to faces ABC and DEF • edges AD, CF and BE have length h cm Given that the volume of the toy is 240 cm3 (a) show that the surface area of the toy, S cm2 , is given by 1680 S = 0.8r2 + r making your method clear. (4) Using algebraic differentiation, (b) find the value of r for which S has a stationary point. (4) (c) Prove, by further differentiation, that this value of r gives the minimum surface area of the toy. (2)

Lesson: Definitions of Sine, Cosine and Tangent and Exact Values