# Cone

Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.

Correct result:

V =  565.5 cm3
S =  463.7 cm2

#### Solution:

$D=15 \ \text{cm} \ \\ r=D/2=15/2=\dfrac{ 15 }{ 2 }=7.5 \ \text{cm} \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 7.5^2 \doteq 176.7146 \ \text{cm}^2 \ \\ A=52 \ ^\circ \ \\ h=r \cdot \ \tan A ^\circ =r \cdot \ \tan 52^\circ \ =7.5 \cdot \ \tan 52^\circ \ =7.5 \cdot \ 1.279942=9.59956 \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 176.7146 \cdot \ 9.5996=565.5 \ \text{cm}^3$
$s=\sqrt{ h^2 + r^2 }=\sqrt{ 9.5996^2 + 7.5^2 } \doteq 12.182 \ \text{cm} \ \\ S=S_{1} + \pi \cdot \ r \cdot \ s=176.7146 + 3.1416 \cdot \ 7.5 \cdot \ 12.182=463.7 \ \text{cm}^2$ 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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