Multiple choice

From a right circular cylinder of radius 6 cm and height 11 cm one hemisphere of the same radius is removed then the volume of the remaining part is

  1. 792 $ \displaystyle cm^{3} $
  2. 892 $ \displaystyle cm^{3} $
  3. 992 $ \displaystyle cm^{3} $

  4. none of these
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A Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 6^2 * 11 = 396 * pi. Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * pi * 6^3 = 144 * pi. Remaining volume = 396 * pi - 144 * pi = 252 * pi. Using pi approx 3.14, 252 * 3.14 = 791.28, which rounds to 792.

AI explanation

Using the volume of a cylinder formula V = pi r^2 h, the initial volume is pi times 6 squared times 11, which equals 396 pi. The volume of the removed hemisphere is found using two-thirds pi r^3, giving two-thirds pi times 6 cubed, resulting in 144 pi. Subtracting the hemisphere from the cylinder yields 396 pi minus 144 pi, leaving 252 pi, which calculates to 252 times 3.14 or approximately 792 cm^3.

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