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 cm3 h=15 cm  V=13 π r02 h  r0=3 Vπ h=3 56993.1416 1519.0476 cm  r=23 r0=23 19.047612.6984=12.7  cm 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=2π r=2 3.1416 12.698479.7965=79.8  cm o = 2 \pi \cdot \ r = 2 \cdot \ 3.1416 \cdot \ 12.6984 \doteq 79.7965 = 79.8 \ \text{ cm }



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Math student
The solution that you give us doesn't make sense.

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Dr Math
... and what is bad or unclear? What is your solution?

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