Triangle cone rotation

A thin plate in the shape of a right-angled triangle is turned once around the shorter hanger and a second time around the longer hanger. Cones are described by rotation. Are they the same volume? The dimensions are: shorter pendant 6 cm, longer pendant 8 cm.

Final Answer:

V₁ =  301.5929 cm³
V₂ =  402.1239 cm³

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ b=8\text{cm} \\ {r}_1=a=6\text{cm} \\ {h}_1=b=8\text{cm} \\ {V}_1=\frac{1}{3}\cdot \pi \cdot r_1^2\cdot h_1=\frac{1}{3}\cdot 3.1416\cdot 6^2\cdot 8=301.5929{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} r_2=b=8\text{cm} \\ {h}_2=a=6\text{cm} \\ {V}_2=\frac{1}{3}\cdot \pi \cdot r_2^2\cdot h_2=\frac{1}{3}\cdot 3.1416\cdot 8^2\cdot 6\doteq 402.1239 \\ {V}_2=V_1\ne V_2=402.1239{\text{cm}}^3 \end{gathered}$$

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