Rotary cone

A rotary cone whose height is equal to the circumference of the base has a volume 2488 cm³.

Calculate the radius of the base circle and the height of the cone.

Final Answer:

r =  7.23 cm
h =  45.44 cm

Step-by-step explanation:

$$\begin{gathered} V=2488{\text{cm}}^3 \\ V=\frac{1}{3}\pi r^{2}h \\ h=2\pi r \\ V=\frac{2}{3}{\pi }^2{r}^3 \\ r=\sqrt[ \\ 3]{\frac{3\cdot V}{2{\pi }^2}}=\sqrt[ \\ 3]{\frac{3\cdot 2488}{2\cdot 3.1416^2}}=7.23\text{cm} \end{gathered}$$

$$\begin{gathered} h=2\pi \cdot r=2\cdot 3.1416\cdot 7.2313\doteq 45.4353\text{cm} \\ \text{ Verifying Solution: } \\ {V}_2=\frac{1}{3}\cdot \pi \cdot r^2\cdot h=\frac{1}{3}\cdot 3.1416\cdot 7.2313^2\cdot 45.4353=2488{\text{cm}}^3 \end{gathered}$$

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