Rotating cone

Find the rotating cone's surface and volume if its side is 150 mm long and the circumference of the base is 43.96 cm.

Correct answer:

S =  483.482 cm²
V =  680.1455 cm³

Step-by-step explanation:

$$\begin{gathered} s=150\text{ mm}\to \text{ cm}=150\mathrm{/}10\text{ cm}=15\text{ cm } \\ o=43.96\text{ cm } \\ r=o\mathrm{/}(2\pi )=43.96\mathrm{/}(2\cdot 3.1416)\doteq 6.9965\text{ cm } \\ {s}^2=h^2+r^2 \\ h=\sqrt{s^2-r^2}=\sqrt{15^2-6.9965^2}\doteq 13.2684\text{ cm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 6.9965^2\doteq 153.782{\text{cm}}^2 \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 6.9965\cdot 15={\displaystyle \frac{3297}{10}}=329.7 \\ S=S_1+S_2=153.782+329.7=483.482{\text{cm}}^2 \end{gathered}$$

$V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 153.782\cdot 13.2684=680.1455{\text{cm}}^3$

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