Multiple choice

The volume of a largest sphere that can be cut from cylindrical log of wood of base radius $1 m$ and height $4 m$ is:

  1. $\dfrac{8}{3} \pi\  m^{3}$
  2. $\dfrac{10}{3} \pi\  m^{3}$
  3. $\dfrac{16}{3} \pi\  m^{3}$
  4. $\dfrac{4}{3} \pi\  m^{3}$
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D Correct answer
Explanation

The largest sphere that can be cut from a cylinder is limited by the smaller of the base diameter or the height. Here, the base radius is 1m (diameter 2m) and height is 4m. The sphere's diameter must be 2m, so radius r = 1m. Volume = 4/3 * pi * r^3 = 4/3 * pi * 1^3 = 4/3 pi.

AI explanation

The largest sphere that can be cut from a cylindrical log of base radius 1 m and height 4 m is restricted by the cylinder's diameter, giving the sphere a maximum radius of 1 m. Using the sphere volume formula V = (4/3) * pi * r^3, the volume is (4/3) * pi * 1^3. The result is 4/3 * pi cubic meters.

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