CAIE IGCSE Mathematics Extended similar lengths, areas and volumes

Practise using length, area, surface area and volume scale factors to solve problems with similar shapes, solids and containers.

Exam points

convert an area ratio into a length scale factor before finding a missing height
apply cubed scale factors to volumes, capacities or masses of similar solids
use surface area and volume data together when a similar solid has extra context

[Maximum number: 3]

A sector of a circle has radius 8 cm and area 160 cm^2.

A mathematically similar sector has radius 20 cm .
Calculate the area of the larger sector.
cm^2
[3]

1000 cao
M2 for $160\times\left(\frac{20}{8}\right)^2$ or $160\div\left(\frac{8}{20}\right)^2$ oe
or M1 for $\left(\frac{20}{8}\right)^2$ or $\left(\frac{8}{20}\right)^2$ oe

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E4.4.2 Use the relationships between lengths and areas of similar shapes and question 1