Multiple choice

A cone of height 10 cm and radius 10 cm is to be divided into two parts by cutting through the mid point of the vertical axis Then the volume of the conical part is

  1. $ \displaystyle \frac{1000}{3}\pi cm^{3} $
  2. $ \displaystyle \frac{500}{3}\pi cm^{3} $
  3. $ \displaystyle \frac{250}{3}\pi cm^{3} $
  4. $ \displaystyle \frac{125}{3}\pi cm^{3} $
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D Correct answer
Explanation

The cone is cut at the midpoint of the height. The smaller cone has height 5 and radius 5 (by similar triangles). Volume = (1/3) * pi * r^2 * h = (1/3) * pi * 5^2 * 5 = 125/3 * pi.

AI explanation

Cutting the cone through the midpoint of its vertical axis creates a smaller, similar cone with half the original height, making the new height 5 cm. Because the radius scales proportionally with the height in similar figures, the radius of this smaller conical part is also halved to 5 cm. Using the cone volume formula, which is one third times pi times the radius squared times the height, the calculation is one third times pi times 5 squared times 5. This simplifies to one third times pi times 125, resulting in a volume of 125 divided by 3 times pi.

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