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Date May 2019 Marks available 2 Reference code 19M.1.SL.TZ1.T_15
Level Standard Level Paper Paper 1 Time zone Time zone 1
Command term Find Question number T_15 Adapted from N/A

Question

A cylinder with radius r and height h is shown in the following diagram.

The sum of r and h for this cylinder is 12 cm.

Write down an equation for the area, A, of the curved surface in terms of r.

[2]
a.

Find dAdr.

[2]
b.

Find the value of r when the area of the curved surface is maximized.

[2]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

A=2πr(12r)  OR  A=24πr2πr2        (A1)(M1)  (C2)

Note: Award (A1) for  r+h=12  or  h=12r  seen. Award (M1) for correctly substituting into curved surface area of a cylinder. Accept A=2πr(12r)  OR  A=24πr2πr2.

[2 marks]

a.

24π4πr       (A1)(ft)(A1)(ft)  (C2)

Note: Award (A1)(ft) for 24π and  (A1)(ft) for 4πr . Follow through from part (a). Award at most (A1)(ft)(A0) if additional terms are seen.

[2 marks]

b.

24π4πr=0       (M1)

Note: Award (M1) for setting their part (b) equal to zero.

6 (cm)       (A1)(ft)  (C2)

Note: Follow through from part (b).

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 3—Geometry and trigonometry » SL 3.1—3d space, volume, angles, midpoints
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Topic 5—Calculus » SL 5.3—Differentiating polynomials, n E Z
Topic 5—Calculus » SL 5.7—Optimisation
Topic 3—Geometry and trigonometry
Topic 5—Calculus

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