Cone

Calculate the volume and surface area of ​​the cone with a diameter of the base d=16 cm and the side of the cone with the base has angle 37°12'.

Correct answer:

V =  407 cm³
S =  453.5 cm²

Step-by-step explanation:

$$\begin{gathered} D=16\text{cm} \\ r=D/2=16/2=8\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 8^2\doteq 201.0619{\text{cm}}^2 \\ A=37.2{}^{\circ } \\ h=r\cdot \tan A=r\cdot \tan 37.2°=8\cdot \tan 37.2°=8\cdot 0.759041=6.07233\text{cm} \\ V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 201.0619\cdot 6.0723=407{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} s=\sqrt{h^2+r^2}=\sqrt{6.0723^2+8^2}\doteq 10.0436\text{cm} \\ S=S_1+\pi \cdot r\cdot s=201.0619+3.1416\cdot 8\cdot 10.0436=453.5{\text{cm}}^2 \end{gathered}$$

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