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 cm r=D/2=15/2=152=7.5 cm S1=π⋅ r2=3.1416⋅ 7.52≐176.7146 cm2 A=52 ∘ h=r⋅ tan⁡A∘=r⋅ tan⁡52∘ =7.5⋅ tan⁡52∘ =7.5⋅ 1.279942=9.59956 V=13⋅ S1⋅ h=13⋅ 176.7146⋅ 9.5996=565.5 cm3D=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=h2+r2=9.59962+7.52≐12.182 cm S=S1+π⋅ r⋅ s=176.7146+3.1416⋅ 7.5⋅ 12.182=463.7 cm2s=\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

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