Cone

Calculate volume and surface area of ​​the cone with a diameter of the base d=15 cm and side of the 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 cm V=13⋅ S1⋅ h=13⋅ 176.7146⋅ 9.5996=565.5 cm3
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 cm2

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