SPM 2021 Add Maths Paper 1, Question 10Progressions

Diagram 7 shows a roll of aluminium with a length of 55 440 mm that can be cut exactly into 72 sections. The length of the first sheet is x mm and the length of each subsequent sheet increases by 20 mm. Atan is assigned to cut the aluminium roll. State the length, in mm, of the first three aluminium sheets in terms of x.

Atan has completed 2/3 of his task. By determining the value of x, calculate the total length, in mm, of the last 18 sheets that have been cut. (The roll is 55 440 mm, cut into 72 sheets; first sheet x mm, each subsequent sheet 20 mm longer.)

The cut aluminium sheets can be formed into a cylinder open at both ends in two different ways. After Atan completed his (full) task, his brother chose the last sheet to form a cylinder with maximum volume. By calculation, suggest the cylinder that fulfils the condition. (Roll 55 440 mm cut into 72 sheets; first sheet 60 mm, common difference 20 mm; sheet width 500 mm.)