Cylindrical rod

We should grind a cylindrical rod with a diameter of 6 cm and a length of 20 cm to form a conical rod of the same size and the same base diameter. What will be the volume of material removed?

Final Answer:

V =  376.9911 cm³

Step-by-step explanation:

$$\begin{gathered} D=6\text{cm} \\ l=20\text{cm} \\ r=D/2=6/2=3\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3^2\doteq 28.2743{\text{cm}}^2 \\ {V}_1=S_1\cdot l=28.2743\cdot 20\doteq 565.4867{\text{cm}}^3 \\ {V}_2=\frac{1}{3}\cdot S_1\cdot l=\frac{1}{3}\cdot 28.2743\cdot 20\doteq 188.4956{\text{cm}}^3 \\ V=V_1-V_2=565.4867-188.4956=376.9911{\text{cm}}^3 \end{gathered}$$

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