CH-23-001 · Similar solids: volumes, surface areas and coating cost

Diagram not accurately drawn

Two solid models are mathematically similar. The smaller has volume 216 cm³ and surface area 72 cm². The larger has volume 4096 cm³. Coating costs 6 pence per cm². Calculate how much more it costs to coat the larger model than the smaller. Give your answer in pounds.

Similar Shapes: L.A.V Table (Volumes to Surface Areas & Cost) Booklet p. 41

Method

1) Put corresponding measurements in an L.A.V table (or L.L for two lengths)

2) Length factor r, area factor r², volume factor r³

3) Multiply from small to large; divide in reverse

Worked Example (CH-23-001)

Dimension	Small	Scale factor: small → large	Large
V	216	$\frac{512}{27}$	4096
L		$\sqrt[3]{\frac{512}{27}}$
A	72	$(\sqrt[3]{\frac{512}{27}})^2$	512

Extra area:

512-72=440

cm².

Extra cost:

440\times6\div100=26.40

pounds.

Ans = £26.40