Multiple choice

The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius $3$ cm and height $7$ cm is

  1. $108\pi cm^3$
  2. $36 \pi cm^3$
  3. $12\pi cm^3$
  4. $\frac {4}{3}\pi cm^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The greatest sphere that can fit inside a cylinder is limited by the smaller of the cylinder's diameter (2 * radius = 6) or height (7). The diameter of the sphere is 6, so its radius is 3. Volume = (4/3) * pi * r^3 = (4/3) * pi * 27 = 36 * pi.

AI explanation

The greatest sphere that can be cut from a cylindrical log is limited by the smaller of the log's base radius and half of its height. Since the base radius is 3 cm and half of the height is 3.5 cm, the maximum possible radius of the sphere is 3 cm. The volume of a sphere is given by the formula V = (4/3) * pi * r^3, so substituting the radius gives V = (4/3) * pi * 3^3. Calculating this results in a volume of 36 * pi cubic centimeters.

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