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The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base and its volume is 1/64 the volume of original cone. What is the height from the base at which the section is made?

The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base and its volume is 1/64 the volume of original cone. What is the height from the base at which the section is made? Correct Answer 45 cm

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In the figure, R and r are the radius of the two cones and H and h are the heights;

∴ r/R = h/H

Volume of new cone : Volume of original cone = 1 : 64;

∴ 1/3(πr2h) : 1/3(πR2H) = 1 : 64

⇒ r2h : R2H = 1 : 64

Putting r/R = h/H;

⇒ h3 : H3 = 1 : 64

⇒ h : H = 1 : 4

∵ H = 60 cm (Given)

∴ h = 60/4 = 15 cm

∴ Height from the base at which the section is made = H – h = 60 – 15 = 45 cm

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