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Date November 2016 Marks available 3 Reference code 16N.2.SL.TZ0.S_6
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Question number S_6 Adapted from N/A

Question

All lengths in this question are in metres.

Let f ( x ) = 0.8 x 2 + 0.5 , for 0.5 x 0.5 . Mark uses f ( x ) as a model to create a barrel. The region enclosed by the graph of f , the x -axis, the line x = 0.5 and the line x = 0.5 is rotated 360° about the x -axis. This is shown in the following diagram.

N16/5/MATME/SP2/ENG/TZ0/06

Use the model to find the volume of the barrel.

[3]
a.

The empty barrel is being filled with water. The volume V   m 3  of water in the barrel after t minutes is given by V = 0.8 ( 1 e 0.1 t ) . How long will it take for the barrel to be half-full?

[3]
b.

Markscheme

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

attempt to substitute correct limits or the function into the formula involving

y 2

eg π 0.5 0.5 y 2 d x ,   π ( 0.8 x 2 + 0.5 ) 2 d x

0.601091

volume = 0.601   ( m 3 )      A2     N3

[3 marks]

a.

attempt to equate half their volume to V     (M1)

eg 0.30055 = 0.8 ( 1 e 0.1 t ) , graph

4.71104

4.71 (minutes)     A2     N3

[3 marks]

b.

Examiners report

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

Syllabus sections

Topic 5—Calculus » SL 5.5—Integration introduction, areas between curve and x axis
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