# Cone

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 result:

r =  12.7 cm
o =  79.8 cm

#### Solution:

$V=5699 \ \text{cm}^3 \ \\ h=15 \ \text{cm} \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r_{0}^2 \cdot \ h \ \\ \ \\ r_{0}=\sqrt{ \dfrac{ 3 \cdot \ V }{ \pi \cdot \ h } }=\sqrt{ \dfrac{ 3 \cdot \ 5699 }{ 3.1416 \cdot \ 15 } } \doteq 19.0476 \ \text{cm} \ \\ \ \\ r=\dfrac{ 2 }{ 3 } \cdot \ r_{0}=\dfrac{ 2 }{ 3 } \cdot \ 19.0476=12.7 \ \text{cm}$
$o=2 \pi \cdot \ r=2 \cdot \ 3.1416 \cdot \ 12.6984=79.8 \ \text{cm}$

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