18N.1.SL.TZ0.T_9

pestleMathematicsAISLPaper 118N· sl-3-1-3d-space-volume-angles-midpointssource ↗

A solid glass paperweight consists of a hemisphere of diameter 6 cm on top of a cuboid with a square base of length 6 cm, as shown in the diagram.

The height of the cuboid, x cm, is equal to the height of the hemisphere.

Write down the value of x.

[1]

a.i.

Calculate the volume of the paperweight.

[3]

a.ii.

1 cm³ of glass has a mass of 2.56 grams.

Calculate the mass, in grams, of the paperweight.

[2]

Markscheme / solution

3 (cm) (A1) (C1)

[1 mark]

a.i.

units are required in part (a)(ii)

$\frac{1}{2} \times \frac{{4\pi \times {{\left( 3 \right)}^3}}}{3} + 3 \times {\left( 6 \right)^2}$ (M1)(M1)

Note: Award (M1) for their correct substitution in volume of sphere formula divided by 2, (M1) for adding their correctly substituted volume of the cuboid.

= 165 cm³(164.548…) (A1)(ft) (C3)

Note: The answer is 165 cm³; the units are required. Follow through from part (a)(i).

[3 marks]

a.ii.

their 164.548… × 2.56 (M1)

Note: Award (M1) for multiplying their part (a)(ii) by 2.56.

= 421 (g) (421.244…(g)) (A1)(ft) (C2)

Note: Follow through from part (a)(ii).

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]