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Similar solids and scaling volume

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
Cuboids; surface area scalingCuboids; volume scalingNOWMix of allRecommended
Question 1 of 8

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Solid A and solid B are cuboids in a set of packaging prototypes

Solid A: length 12 cm, width 16 cm, height 18 cm. Solid B: length 36 cm, width 58 cm, height 54 cm. Each measurement names the corresponding linear role shown

Solid A. Solid A and Solid B are cuboids. Corresponding dimensions are labelled. The panels use separate drawing scales; compare the measurements.lwhSolid ASolid B. Solid A and Solid B are cuboids. Corresponding dimensions are labelled. The panels use separate drawing scales; compare the measurements.lwhSolid B
Separate drawing scales. Compare corresponding measurements, not the displayed sizes
(a)1 mark

Are solid A and solid B similar? Select the verdict with the complete ratio reason

(b)1 mark

Using the corresponding length, calculate the proposed linear scale factor \(k\) from solid A to solid B

Format: Exact number or fraction
(c)1 mark

If every dimension followed the proposed \(k\), calculate the surface-area factor \(k^2\)

Format: Exact number or fraction