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

User interface language: English | Español

Date May 2017 Marks available 2 Reference code 17M.1.sl.TZ2.12
Level SL only Paper 1 Time zone TZ2
Command term Find Question number 12 Adapted from N/A

Question

A cylindrical container with a radius of 8 cm is placed on a flat surface. The container is filled with water to a height of 12 cm, as shown in the following diagram.

M17/5/MATSD/SP1/ENG/TZ2/12

A heavy ball with a radius of 2.9 cm is dropped into the container. As a result, the height of the water increases to h cm, as shown in the following diagram.

M17/5/MATSD/SP1/ENG/TZ2/12.b

Find the volume of water in the container.

[2]
a.

Find the value of h.

[4]
b.

Markscheme

π×82×12     (M1)

 

Note:     Award (M1) for correct substitution into the volume of a cylinder formula.

 

2410 cm3 (2412.74 cm3, 768π cm3)     (A1)     (C2)

[2 marks]

a.

43π×2.93+768π=π×82h     (M1)(M1)(M1)

 

Note:     Award (M1) for correct substitution into the volume of a sphere formula (this may be implied by seeing 102.160…), (M1) for adding their volume of the ball to their part (a), (M1) for equating a volume to the volume of a cylinder with a height of h.

 

OR

43π×2.93=π×82(h12)     (M1)(M1)(M1)

 

Note:     Award (M1) for correct substitution into the volume of a sphere formula (this may be implied by seeing 102.160…), (M1) for equating to the volume of a cylinder, (M1) for the height of the water level increase, h12. Accept h for h12 if adding 12 is implied by their answer.

 

(h=) 12.5 (cm) (12.5081 (cm))     (A1)(ft)     (C4)

 

Note:     If 3 sf answer used, answer is 12.5 (12.4944…). Follow through from part (a) if first method is used.

 

[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