Multiple choice

A cone of height $9 \ cm$ with diameter of its base is curved out from a wooden solid sphere of radius $9 \ cm$. The percentage of wood wasted is.

  1. $25\%$
  2. $25.5\%$
  3. $50\%$
  4. $75\%$
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D Correct answer
Explanation

Volume of sphere = (4/3)*pi*r^3 = (4/3)*pi*9^3 = 972*pi. Volume of cone = (1/3)*pi*r^2*h = (1/3)*pi*9^2*9 = 243*pi. Wasted volume = 972*pi - 243*pi = 729*pi. Percentage wasted = (729/972) * 100 = 75%.

AI explanation

The volume of the wooden solid sphere is found using the formula (4/3) * pi * R^3, which equals (4/3) * pi * 9^3 = 972 pi cubic cm. The volume of the cone curved out is (1/3) * pi * r^2 * h, where the base radius is 9 cm and the height is 9 cm, giving (1/3) * pi * 81 * 9 = 243 pi cubic cm. The wood wasted is the difference between the two volumes, which is 972 pi - 243 pi = 729 pi cubic cm. The percentage of wood wasted is (729 pi / 972 pi) * 100, resulting in 75%.

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