Composite solids can be formed by either

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Presentation transcript:

Composite solids can be formed by either (i) combining two or more shapes. (ii) removing one solid from another. Ex A grain silo consists of a cylinder of diameter 6m and height 8m topped by a hemisphere. For both cylinder & hemisphere d = 6 so r = 3. Vol cylinder = r2h = 3.14 X 3 X 3 X 8 = 226.08 8m Vol h-sphere = 2/3 r3 = 2 X 3.14 X 3 X 3 X 3  3 = 56.52 Total vol = 226.08 + 56.52 = 282.6 = 283m3 6m

A “Polo” mint is 4mm thick with a diameter of 12mm. Example A “Polo” mint is 4mm thick with a diameter of 12mm. The hole is 6mm in diameter. Find the total vol of mint. 4mm 6mm 12mm NB: the mint is a “big cylinder – a wee cylinder”. Big C. d = 12 so r = 6 & h = 4 V = r2h = 3.14 X 6 X 6 X 4 = 452.16 Wee C. d = 6 so r = 3 & h = 4 V = r2h = 3.14 X 3 X 3 X 4 = 113.04 Vol mint = 452.16 – 113.04 = 339.12 = 339mm3