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 the 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

Question

Vikas TU · Answer

As the qstn. has been asked twice. Re-posting the answer: 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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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 the 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 the 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

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