Volume of the cone

Find the volume of the cone with the base radius r and the height v.
a) r = 6 cm, v = 8 cm
b) r = 0,9 m, v = 2,3 m
c) r = 1,4 dm, v = 30 dm

Final Answer:

V₁ =  301.5929 cm³
V₂ =  1.9509 m³
V₃ =  61.5752 dm³

Step-by-step explanation:

$$\begin{gathered} r_1=6\text{cm} \\ {v}_1=8\text{cm} \\ {V}_1=\frac{1}{3}\cdot \pi \cdot r_1^2\cdot v_1=\frac{1}{3}\cdot 3.1416\cdot 6^2\cdot 8=301.5929{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} r_2=0.9\text{m} \\ {v}_2=2.3\text{m} \\ {V}_2=\frac{1}{3}\cdot \pi \cdot r_2^2\cdot v_2=\frac{1}{3}\cdot 3.1416\cdot 0.9^2\cdot 2.3=1.9509{\text{m}}^3 \end{gathered}$$

$$\begin{gathered} r_3=1.4\text{dm} \\ {v}_3=30\text{dm} \\ {V}_3=\frac{1}{3}\cdot \pi \cdot r_3^2\cdot v_3=\frac{1}{3}\cdot 3.1416\cdot 1.4^2\cdot 30=61.5752{\text{dm}}^3 \end{gathered}$$

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