18N.1.SL.TZ0.T_1

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

The volume of a hemisphere, V, is given by the formula

V = $\sqrt {\frac{{4\,{S^3}}}{{243\,\pi }}}$ ,

where S is the total surface area.

The total surface area of a given hemisphere is 350 cm².

Calculate the volume of this hemisphere in cm³.

Give your answer correct to one decimal place.

[3]

Write down your answer to part (a) correct to the nearest integer.

[1]

Write down your answer to part (b) in the form a × 10^k , where 1 ≤ a < 10 and k ∈ $\mathbb{Z}$ .

[2]

Markscheme / solution

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

$\sqrt {\frac{{4\,{{\left( {350} \right)}^3}}}{{243\,\pi }}}$ OR $\sqrt {\frac{{171500\,000}}{{763.407\, \ldots }}}$ (M1)

Note: Award (M1) for substitution of 350 into volume formula.

= 473.973… (A1)

= 474 (cm³) (A1)(ft) (C3)

Note: The final (A1)(ft) is awarded for rounding their answer to 1 decimal place provided the unrounded answer is seen.

[3 marks]

474 (cm³) (A1)(ft) (C1)

Note: Follow through from part (a).

[1 mark]

4.74 × 10² (cm³) (A1)(ft)(A1)(ft) (C2)

Note: Follow through from part (b) only.

Award (A0)(A0) for answers of the type 0.474 × 10³.

[2 marks]

Examiners’ report

[N/A]