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The height of a cone is 24cm. A small cone is cut from the portion of vertex by a plane perpendicular to the axis of cone. The volume of this small cone is 1/64 of the original cone. Find at what distance from the base,the small cone is cut .

The height of a cone is 24cm. A small cone is cut from the portion of vertex by a plane perpendicular to the axis of cone. The volume of this small cone is 1/64 of the original cone. Find at what distance from the base,the small cone is cut .

Grade:10

1 Answers

Vikas TU
14149 Points
4 years ago
let at h distance from base it is cut then,
Volume of this cut cone = > (1/3)*pi*r^2(24-h) cm^3 = V
Volume of original cone = > V’ = (1/3) * pi* R^2 * 24 
dividing the V and V’ we get,
V/V’ = (r/R)^2 * (24-h)/24 = > 1/64
 
Now from similar triangles in small and cutted cone we get the relation inheight and radii are:
r/R = (24 – h)/24
[(24 – h)/24]^3 = 1/64
(24-h)/24 = ¼
24 – h = 6
h = 18 cm.

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