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°.

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 7.52176.7146 cm2 A=52  h=r tan(Arad=A π180 rad=9.59956224145 rad) V=13 S1 h=13 176.7146 9.5996565.4609=565.5 cm3D = 15 \ cm \ \\ r = D/2 = 15/2 = \frac{ 15 }{ 2 } = 7.5 \ cm \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 7.5^2 \doteq 176.7146 \ cm^2 \ \\ A = 52 \ ^\circ \ \\ h = r \cdot \ \tan( A \rightarrow rad = A \cdot \ \frac{ \pi }{ 180 } \ rad = 9.59956224145 \ rad) \ \\ V = \frac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h = \frac{ 1 }{ 3 } \cdot \ 176.7146 \cdot \ 9.5996 \doteq 565.4609 = 565.5 \ cm^3
s=h2+r2=9.59962+7.5212.182 cm S=S1+π r s=176.7146+3.1416 7.5 12.182463.7467=463.7 cm2s = \sqrt{ h^2 + r^2 } = \sqrt{ 9.5996^2 + 7.5^2 } \doteq 12.182 \ cm \ \\ S = S_{ 1 } + \pi \cdot \ r \cdot \ s = 176.7146 + 3.1416 \cdot \ 7.5 \cdot \ 12.182 \doteq 463.7467 = 463.7 \ cm^2







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Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.