Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js

User interface language: English | Español

Date November 2016 Marks available 4 Reference code 16N.1.sl.TZ0.7
Level SL only Paper 1 Time zone TZ0
Command term Calculate Question number 7 Adapted from N/A

Question

A balloon in the shape of a sphere is filled with helium until the radius is 6 cm.

The volume of the balloon is increased by 40%.

Calculate the volume of the balloon.

[2]
a.

Calculate the radius of the balloon following this increase.

[4]
b.

Markscheme

Units are required in parts (a) and (b).

43π×63    (M1)

 

Note:     Award (M1) for correct substitution into volume of sphere formula.

 

=905 cm3 (288π cm3, 904.778 cm3)    (A1)     (C2)

 

Note:     Answers derived from the use of approximations of π (3.14; 22/7) are awarded (A0).

 

[2 marks]

a.

Units are required in parts (a) and (b).

140100×904.778=43πr3 OR 140100×288π=43πr3 OR 1266.69=43πr3     (M1)(M1)

 

Note:     Award (M1) for multiplying their part (a) by 1.4 or equivalent, (M1) for equating to the volume of a sphere formula.

 

r3=3×1266.694π OR r=33×1266.694π OR r=3(1.4)×63 OR r3=302.4     (M1)

 

Note:     Award (M1) for isolating r.

 

(r=) 6.71 cm (6.71213)     (A1)(ft)     (C4)

 

Note:     Follow through from part (a).

 

[4 marks]

b.

Examiners report

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

Syllabus sections

Topic 5 - Geometry and trigonometry » 5.5
Show 126 related questions

View options