Edexcel IGCSE Math A 4.11.HB volume ratios in similar figures

Practise the similar-volume question by cubing the linear scale factor and writing the volume of one vase in terms of V.

Exam points

Cube the linear scale factor before comparing volumes of similar figures.

[Maximum number: 2]

17 A and B are two similar vases.

Figure for Question 4.11.HB Volume scale factors question 1 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

Vase A has height 24 cm.
Vase B has height 36 cm.
Vase A has a surface area of $960 \mathrm{~cm}^{2}$

Find in terms of V, an expression for the volume, in $\mathrm{cm}^{3}$ , of vase A.
$\mathrm{cm}^{3}$

$\left(\frac{24}{36}\right)^3$
or
$2^3:3^3$
oe, or reciprocal equivalents.

Final answer:
$\frac{8}{27}V$
oe, e.g.
$\frac{V}{3.375}$

Marking guidance:
- M1 for correct scale factor for volume, ft from linear scale factor in part (a) or ft from $\sqrt{2160/960}$
- A1 for $\frac{8}{27}V$ oe

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4.11.HB Volume scale factors question 1