Multiple choice

The volume of the greatest sphere cut off from a cylindrical wood of base radius 1 cm and height 5 cm is

  1. $ \displaystyle \frac{4}{3}\times (5\pi )cm^{3} $
  2. $ \displaystyle \frac{4}{3} \pi cm^{3} $
  3. $ \displaystyle 5\pi cm^{3} $
  4. $ \displaystyle \frac{10\pi }{3}cm^{3} $
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B Correct answer
Explanation

The greatest sphere that can be cut from a cylinder of radius 1 cm and height 5 cm is limited by the radius. The sphere's radius is 1 cm. Volume = (4/3) * pi * r^3 = (4/3) * pi * 1^3 = (4/3) * pi.

AI explanation

The greatest sphere that can be cut from a cylinder is limited by the cylinder's smaller dimension, which is its base radius of 1 cm. This means the maximum possible diameter of the sphere is 2 cm, giving it a radius of 1 cm. Using the sphere volume formula of (4/3) * pi * r^3, we substitute r = 1 to get (4/3) * pi cubic centimeters.

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