Parameters 28521

The basic parameters of the rotating cone are:
Base radius 5 cm
The cone height is 12 cm, and the cone side is 13 cm.
Calculate:
a/volume of the cone
b/cone surface

Correct answer:

V =  314.1593 cm³
S =  282.7433 cm²

Step-by-step explanation:

$$\begin{gathered} r=5\text{cm} \\ h=12\text{cm} \\ s=13\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 5^2\doteq 78.5398{\text{cm}}^2 \\ V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 78.5398\cdot 12=314.1593{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_2=\pi \cdot r\cdot s=3.1416\cdot 5\cdot 13\doteq 204.2035{\text{cm}}^2 \\ S=S_1+S_2=78.5398+204.2035\doteq 282.7433{\text{cm}}^2 \\ \text{ Verifying Solution: } \\ {s}^2=h^2+r^2 \\ {s}_2=\sqrt{h^2+r^2}=\sqrt{12^2+5^2}=13\text{cm} \end{gathered}$$

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