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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?
  • a)
    15 cm
  • b)
    20 cm
  • c)
    30 cm
  • d)
    45 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The height of a cone is 60 cm. A small cone is cut off at the top by a...

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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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?a)15 cmb)20 cmc)30 cmd)45 cmCorrect answer is option 'D'. Can you explain this answer?
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