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Doctors Medicines MCQs Q&A

  1. 2 cm
  2. 3 cm
  3. 4 cm
  4. 6 cm
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1 Answers

Option 2 : 3 cm

Given:

The volume of the full cone is 125 times the volume of the smaller cone formed. The height of the full cone is 15 cm.

Formula Used:

By using similarity we can prove that the volume of a cone when cuts by a plane are given by

V(upper cone)/V(full cone) = (r/R)3 = (h/H)3

Where r, h is the radii and height formed by the plane, and R, H is the radii and height of the base.

Calculation:

Let the Height of the full cone be H cm and of the smaller cone be h cm.

The volume of the full cone/ Volume of the smaller cone = 125/1

⇒ This volume ratio = (Height of the full cone/ Height of the smaller cone)3

Taking cube root both sides we get

⇒ 5/1 = H/h or H = 5h

As given full height is 15 cm = H,

The value of height of smaller cone = 15/5 = 3 cm

∴ The height of the smaller cone is 3 cm

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