Cone area and side

Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.

Correct answer:

S =  1983.3983 dm²
V =  412.6973 l

Step-by-step explanation:

$$\begin{gathered} h=1.25 \\ s=17.8 \\ r=\sqrt{s^2-h^2}=\sqrt{17.8^2-1.25^2}\doteq 17.7561 \\ {S}_1=\pi \cdot r^2=3.1416\cdot 17.7561^2\doteq 990.4735 \\ S=S_1+\pi \cdot r\cdot s=990.4735+3.1416\cdot 17.7561\cdot 17.8=1983.3983{\text{dm}}^2 \end{gathered}$$

$V=S_1\cdot h\mathrm{/}3=990.4735\cdot 1.25\mathrm{/}3=412.6973\text{ l}$

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