19M.1.SL.TZ1.T_6

pestleMathematicsAISLPaper 119M· sl-3-1-3d-space-volume-angles-midpointssource ↗

Money boxes are coin containers used by children and come in a variety of shapes. The money box shown is in the shape of a cylinder. It has a radius of 4.43 cm and a height of 12.2 cm.

Find the volume of the money box.

[3]

A second money box is in the shape of a sphere and has the same volume as the cylindrical money box.

Find the diameter of the second money box.

[3]

Markscheme / solution

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

(V =) $\pi {\left( {4.43} \right)^2} \times 12.2$ (M1)(A1)

Note: Award (M1) for substitution into volume of a cylinder formula, (A1) for correct substitution.

752 cm³ (752.171…cm³) (A1)(C3)

[3 marks]

$752.171 \ldots = \frac{4}{3}\pi {\left( r \right)^3}$ (M1)

Note: Award (M1) for equating their volume to the volume of a sphere formula.

$\left( {r = } \right)$ 5.64169…cm (A1)(ft)

Note: Follow through from part (a).

$\left( {d = } \right)$ 11.3 cm (11.2833…cm) (A1)(ft) (C3)

[3 marks]

Examiners’ report

[N/A]