Edexcel IGCSE Math A 4.11.HC similar area and volume problems

Practise similar-area-volume questions by finding the linear scale factor, then squaring or cubing it for the quantity required.

Exam points

Use squared scale factors for areas and cubed scale factors for volumes.
Find a missing surface area or volume from tables, ratios or model information.
Combine area and volume relationships in similar solids before solving.

[Maximum number: 3]

Shape P is similar to shape Q
The table shows some information about shape P and shape Q

Table for Question 4.11.HC Areas and volumes of similar figures question 1 — Edexcel IGCSE Math A Higher

Work out the volume of shape Q

Surface area scale factor:
$\frac{450}{200}=\frac{9}{4}$
Linear scale factor:
$\left(\frac{3}{2}\right)^2=\frac{9}{4} \quad\Rightarrow\quad \text{linear scale factor}=\frac{3}{2}$
Volume scale factor:
$\left(\frac{3}{2}\right)^3=\frac{27}{8}$ $672\times\frac{27}{8}=2268$

Final answer:
$2268\text{ cm}^3$

M1 for using the surface-area ratio. M1 for the linear scale factor. M1 for the volume scale factor. A1 cao.

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4.11.HC Areas and volumes of similar figures question 1