Rotary cone

A rotary cone whose height is equal to the circumference of the base has a volume 229 cm³.

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

Correct answer:

r =  3.26 cm
h =  20.51 cm

Step-by-step explanation:

$$\begin{gathered} V=\frac{1}{3}\pi r^{2}h=229c{m}^3 \\ h=2\pi r \\ V=\frac{2}{3}{\pi }^2{r}^3 \\ r=\sqrt[3]{\frac{3}{2}\frac{V}{{\pi }^2}}=3.26\text{cm} \end{gathered}$$

$h=2\pi r=20.51\text{cm}$

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