Area and volume > Area solids
1234Area solids

## Solutions to the exercises

Exercise 1

Left figure: area $=\frac{1}{2}\cdot \pi \cdot 1,5\cdot \sqrt{{1,5}^{2}+{3}^{2}}+\frac{1}{2}\cdot \pi \cdot {1,5}^{2}\approx 11,44$ .
Middle figure: area $=\frac{1}{4}\cdot 4\pi \cdot {1,5}^{2}+2\cdot \frac{1}{2}\cdot \pi \cdot {1,5}^{2}=4,5\pi \approx 14,14$ .
Right figure: area $=2\cdot \left(\pi \cdot 1,5\cdot \sqrt{{1,5}^{2}+{1,25}^{2}}-\pi \cdot 0,5\cdot \sqrt{{0,5}^{2}+{0,75}^{2}}\right)+2\cdot \pi \cdot {1,5}^{2}\approx 25,64$ .

Exercise 2

Area $=2\cdot \frac{1}{2}\cdot 8\cdot \sqrt{34}+2\cdot \frac{1}{2}\cdot \left(12+6\right)\cdot \sqrt{41}=8\sqrt{34}+18\sqrt{41}$.

Exercise 3

Area $=5\cdot \frac{1}{2}\cdot 4\cdot \sqrt{{4}^{2}-{2}^{2}}+5\cdot \frac{1}{2}\cdot 4\cdot \frac{2}{tan\left(36\right)}\approx 62,17$.

Exercise 4

area $=\pi \cdot 1,5\cdot \sqrt{{1,5}^{2}+{1}^{2}}+\pi \cdot 2\cdot \sqrt{{12}^{2}+{2}^{2}}-\pi \cdot 1,5\cdot \sqrt{{1,5}^{2}+{9}^{2}\right)}\approx 43,13$.

Exercise 5

area $=\frac{3}{4}\cdot \pi \cdot {119}^{2}-\frac{3}{4}\cdot \pi \cdot {19}^{2}\approx 32515,5$ cm2.

Exercise 6

The figure consists of two regular octagons and $16$ equilateral triangles with edges $4$ cm long.
area $=2\cdot 8\cdot \frac{1}{2}\cdot 4\cdot \frac{2}{tan\left(22,5°\right)}+16\cdot \frac{1}{2}\cdot 4\cdot \sqrt{{4}^{2}-{2}^{2}}\approx 265,36$ .

Exercise 7

area $=4\pi \cdot {4}^{2}-2\cdot \pi \cdot 4\cdot \left(4-\sqrt{{4}^{2}-{3}^{2}}\right)+2\pi \cdot 3\cdot 3\approx 223,6$ m2.