# 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.

Result

r =  12.7 cm
o =  79.8 cm

#### Solution:

$V = 5699 \ cm^3 \ \\ h = 15 \ cm \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r_{ 0 }^2 \cdot \ h \ \\ \ \\ r_{ 0 } = \sqrt{ \dfrac{ 3 \cdot \ V }{ \pi \cdot \ h } } = \sqrt{ \dfrac{ 3 \cdot \ 5699 }{ 3.1416 \cdot \ 15 } } \doteq 19.0476 \ cm \ \\ \ \\ r = \dfrac{ 2 }{ 3 } \cdot \ r_{ 0 } = \dfrac{ 2 }{ 3 } \cdot \ 19.0476 \doteq 12.6984 = 12.7 \ \text { cm }$
$o = 2 \pi \cdot \ r = 2 \cdot \ 3.1416 \cdot \ 12.6984 \doteq 79.7965 = 79.8 \ \text { cm }$

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