The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.
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Answer:
Given,
H = 20 cm = height of the right circular cone.
R cm = radius of the base of the cone
V = Volume of the Cone = 1/3 * π R² * H
Let the radius of the base of the small cone = r cm
h = height of the small cone.
v = volume of small cone = 1/3 π * r² * h
From the similar triangles principles,
r / h = R / H
r = R h / H
given V = 8 v
=> 1/3 π R² H = 8 * 1/3 π r² h
=> R² H = 8 * r² h
=> R² H = 8 * (R² h² / H²) * h
=> H³ = 8 h³
=> h = H/2
=> h = 20 cm / 2 = 10 cm
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