# Cone side

Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.

Result

V =  349.066 cm3
S =  314.159 cm2

#### Solution:

$h = 10 \ cm \ \\ A = 30 ^\circ \rightarrow rad = 30 ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ = 30 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ = 0.5236 \ = π/6 \ \\ \ \\ \tan A = r:h \ \\ \ \\ r = h \cdot \ \tan(A) = 10 \cdot \ \tan(0.5236) \doteq 5.7735 \ cm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 5.7735^2 \doteq 104.7198 \ cm^2 \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 104.7198 \cdot \ 10 \doteq 349.0659 = 349.066 \ cm^3$
$s = \sqrt{ h^2+r^2 } = \sqrt{ 10^2+5.7735^2 } \doteq 11.547 \ cm \ \\ S_{ 2 } = \pi \cdot \ r \cdot \ s = 3.1416 \cdot \ 5.7735 \cdot \ 11.547 \doteq 209.4395 \ cm^2 \ \\ S = S_{ 1 }+S_{ 2 } = 104.7198+209.4395 \doteq 314.1593 = 314.159 \ cm^2$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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