# 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.

Result

S =  1983.398 dm2
V =  412.697 l

#### Solution:

$h=1.25 \ \\ s=17.8 \ \\ r=\sqrt{ s^2-h^2 }=\sqrt{ 17.8^2-1.25^2 } \doteq 17.7561 \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 17.7561^2 \doteq 990.4735 \ \\ S=S_{1} + \pi \cdot \ r \cdot \ s=990.4735 + 3.1416 \cdot \ 17.7561 \cdot \ 17.8 \doteq 1983.3983 \doteq 1983.398 \ \text{dm}^2$
$V=S_{1} \cdot \ h/3=990.4735 \cdot \ 1.25/3 \doteq 412.6973 \doteq 412.697 \ \text{l}$

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