Cone

A circular cone of height 14 cm and volume 4396 cm³ is cut at one third of its height (measured from the base) by a plane parallel to the base. Calculate the radius and circumference of the circular cross-section.

Final Answer:

r =  11.54 cm
o =  72.53 cm

Step-by-step explanation:

$$\begin{gathered} V=4396{\text{cm}}^3 \\ h=14\text{cm} \\ V=\frac{1}{3}\cdot \pi \cdot r_0^2\cdot h \\ {r}_0=\sqrt{\frac{3\cdot V}{\pi \cdot h}}=\sqrt{\frac{3\cdot 4396}{3.1416\cdot 14}}\doteq 17.3161\text{cm} \\ r=\frac{2}{3}\cdot r_0=\frac{2}{3}\cdot 17.3161=11.54\text{cm} \end{gathered}$$

$o=2\pi \cdot r=2\cdot 3.1416\cdot 11.5441=72.53\text{cm}$

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