Multiple choice

If the radius of the base is doubled, keeping the height constant, what is the ratio of the volume of the large cone to the smaller cone?

  1. $4 : 1$
  2. $3 : 1$
  3. $8 : 1$

  4. None of these
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A Correct answer
Explanation

Volume of a cone V = (1/3) * pi * r^2 * h. If r becomes 2r and h remains constant, the new volume V' = (1/3) * pi * (2r)^2 * h = 4 * (1/3) * pi * r^2 * h = 4V. The ratio is 4:1.

AI explanation

Using the cone volume formula V = (1/3) times pi times r squared times h, the original volume is (1/3) times pi times r squared times h. When the radius is doubled, the new volume becomes (1/3) times pi times (2r) squared times h, which simplifies to (4/3) times pi times r squared times h. Comparing the two volumes shows the ratio of the large cone to the smaller cone is 4 : 1.

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