Cone - side

Find the cone's surface area and volume if its height is 125 mm and the side length is 17 cm.

Correct answer:

S =  1032.3877 cm²
V =  1737.6934 cm³

Step-by-step explanation:

$$\begin{gathered} h=125\text{ mm}\to \text{ cm}=125\mathrm{/}10\text{ cm}=12.5\text{ cm } \\ s=17\text{ cm } \\ {s}^2=h^2+r^2 \\ r=\sqrt{s^2-h^2}=\sqrt{17^2-12.5^2}\doteq 11.5217\text{ cm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 11.5217^2\doteq 417.0464{\text{cm}}^2 \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 11.5217\cdot 17\doteq 615.3413 \\ S=S_1+S_2=417.0464+615.3413=1032.3877{\text{cm}}^2 \end{gathered}$$

$V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 417.0464\cdot 12.5=1737.6934{\text{cm}}^3$

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