The rotating

The rotating cone has a height of 0.9 m and the diameter of the base is 7.2 dm. Calculate the surface of the cone. (Hint: use Pythagorean theorem for a side of cone)

Correct result:

S =  150.3436 dm²

Solution:

$$\begin{gathered} h=0.9\text{ m}\to \text{ dm}=0.9\cdot 10\text{ dm}=9\text{ dm } \\ D=7.2\text{ dm } \\ r=D\mathrm{/}2=7.2\mathrm{/}2={\displaystyle \frac{18}{5}}=3.6\text{ dm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3.6^2\doteq 40.715{\text{dm}}^2 \\ s=\sqrt{h^2+r^2}=\sqrt{9^2+3.6^2}\doteq 9.6933\text{ dm } \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 3.6\cdot 9.6933\doteq 109.6286{\text{dm}}^2 \\ S=S_1+S_2=40.715+109.6286=150.3436{\text{dm}}^2 \end{gathered}$$

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