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1234Area solids

Solutions to the exercises

Exercise 1

Left figure: area = 1 2 π 1,5 1,5 2 + 3 2 + 1 2 π 1,5 2 11,44 .
Middle figure: area = 1 4 4 π 1,5 2 + 2 1 2 π 1,5 2 = 4,5 π 14,14 .
Right figure: area = 2 ( π 1,5 1,5 2 + 1,25 2 - π 0,5 0,5 2 + 0,75 2 ) + 2 π 1,5 2 25,64 .

Exercise 2

Area = 2 1 2 8 34 + 2 1 2 ( 12 + 6 ) 41 = 8 34 + 18 41 .

Exercise 3

Area = 5 1 2 4 4 2 - 2 2 + 5 1 2 4 2 tan ( 36 ) 62,17 .

Exercise 4

area = π 1,5 1,5 2 + 1 2 + π 2 12 2 + 2 2 - π 1,5 1,5 2 + 9 2 ) 43,13 .

Exercise 5

area = 3 4 π 119 2 - 3 4 π 19 2 32515,5 cm2.

Exercise 6

The figure consists of two regular octagons and 16 equilateral triangles with edges 4 cm long.
area = 2 8 1 2 4 2 tan ( 22,5 ° ) + 16 1 2 4 4 2 - 2 2 265,36 .

Exercise 7

area = 4 π 4 2 - 2 π 4 ( 4 - 4 2 - 3 2 ) + 2 π 3 3 223,6 m2.

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