Rotating cone

Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.

Correct answer:

V =  2.5483 dm³
S =  33.5672 dm²

Step-by-step explanation:

$$\begin{gathered} r=2.3\text{ dm } \\ v=46\mathrm{/}100={\displaystyle \frac{23}{50}}=0.46\text{ dm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 2.3^2\doteq 16.619{\text{dm}}^2 \\ V=S_1\cdot v\mathrm{/}3=16.619\cdot 0.46\mathrm{/}3=2.5483{\text{dm}}^3 \end{gathered}$$

$$\begin{gathered} s=\sqrt{r^2+v^2}=\sqrt{2.3^2+0.46^2}\doteq 2.3455\text{ dm } \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 2.3\cdot 2.3455\doteq 16.9481{\text{dm}}^2 \\ S=S_1+S_2=16.619+16.9481=33.5672{\text{dm}}^2 \end{gathered}$$

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