Cone

The circular cone of height 15 cm and volume 5699 cm³ is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.

Correct answer:

r =  12.7 cm
o =  79.79 cm

Step-by-step explanation:

$$\begin{gathered} V=5699{\text{cm}}^3 \\ h=15\text{cm} \\ V=\frac{1}{3}\cdot \pi \cdot r_0^2\cdot h \\ {r}_0=\sqrt{\frac{3\cdot V}{\pi \cdot h}}=\sqrt{\frac{3\cdot 5699}{3.1416\cdot 15}}\doteq 19.0476\text{cm} \\ r=\frac{2}{3}\cdot r_0=\frac{2}{3}\cdot 19.0476=12.7\text{cm} \end{gathered}$$

$o=2\pi \cdot r=2\cdot 3.1416\cdot 12.6984=79.79\text{cm}$

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