The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 
of the volume of the given cone, at what height above the base is the section made?
Height of the cone is 30 cm.
Let the height of the cone cut off be h cm
Δ ABE ∼ Δ ACD
Therefore
.............(1)
Volume of the small cone =
th volume of the given cone
× 
= × × 
= × 
(r/R)2 h = 30 ´
(h/H)2 h = 30 ´ ..........[using (1)]
h3 = 30 × 30 × 30 ´
h = 30/3 = 10 cm
Therefore the height of the above section is (30 - 10) cm = 20 cm.
Let the height of the cone cut off be h cm
Δ ABE ∼ Δ ACD
Therefore
.............(1)Volume of the small cone =
th volume of the given cone × = × × = × (r/R)2 h = 30 ´
(h/H)2 h = 30 ´
..........[using (1)]h3 = 30 × 30 × 30 ´
h = 30/3 = 10 cm
Therefore the height of the above section is (30 - 10) cm = 20 cm.
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