Calculate

Calculate the cone's surface and volume from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee.

Correct answer:

S =  560.3027 cm²
V =  508.938 cm³

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ b=9\text{cm} \\ h=a=6\text{cm} \\ r=b=9\text{cm} \\ {s}^2=h^2+r^2 \\ s=\sqrt{h^2+r^2}=\sqrt{6^2+9^2}=3\sqrt{13}\text{cm}\doteq 10.8167\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 9^2\doteq 254.469{\text{cm}}^2 \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 9\cdot 10.8167\doteq 305.8337 \\ S=S_1+S_2=254.469+305.8337=560.3027{\text{cm}}^2 \end{gathered}$$

$V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 254.469\cdot 6=508.938{\text{cm}}^3$

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