Cone volume surface

A right triangle with perpendiculars a = 3 cm and b = 4 cm rotates around a longer perpendicular. Calculate the volume and surface area of the resulting cone.

Final Answer:

S =  75.3982 cm²
V =  37.6991 cm³

Step-by-step explanation:

$$\begin{gathered} a=3\text{cm} \\ b=4\text{cm} \\ b>a \\ r=a=3\text{cm} \\ h=b=4\text{cm} \\ s=\sqrt{r^2+h^2}=\sqrt{3^2+4^2}=5\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3^2\doteq 28.2743{\text{cm}}^2 \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 3\cdot 5\doteq 47.1239{\text{cm}}^2 \\ S=S_1+S_2=28.2743+47.1239=75.3982{\text{cm}}^2 \end{gathered}$$

$V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 28.2743\cdot 4=37.6991{\text{cm}}^3$

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