Cone

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

Correct answer:

V =  565.5 cm³
S =  463.7 cm²

Step-by-step explanation:

$$\begin{gathered} D=15\text{cm} \\ r=D/2=15/2=\frac{15}{2}=7.5\text{cm} \\ {S}_1=\pi \cdot r^2=\pi \cdot {\frac{15}{2}}^2=3.1416\cdot 7.5^2\doteq 176.7146{\text{cm}}^2 \\ A=52{}^{\circ } \\ h=r\cdot \tan A=r\cdot \tan 52°=7.5\cdot \tan 52°=7.5\cdot 1.279942=9.59956\text{cm} \\ V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 176.7146\cdot 9.5996=565.5{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} s=\sqrt{h^2+r^2}=\sqrt{9.5996^2+7.5^2}\doteq 12.182\text{cm} \\ S=S_1+\pi \cdot r\cdot s=S_1+\pi \cdot \frac{15}{2}\cdot s=176.7146+3.1416\cdot 7.5\cdot 12.182=463.7{\text{cm}}^2 \end{gathered}$$

Try another example