Multiple choice

An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of base of each of cone and cylinder is $8 /cm$. The cylindrical part is $240 \ cm$ high and the conical part is $36 \ cm$ high. Find The volume of iron used

  1. $50688{ cm }^{ 3 }$
  2. $42652{ cm }^{ 3 }$
  3. $50878{ cm }^{ 3 }$

  4. None of these
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A Correct answer
Explanation

Volume = Volume of cylinder + Volume of cone. V = pi * r^2 * h_cyl + (1/3) * pi * r^2 * h_cone. V = pi * 8^2 * 240 + (1/3) * pi * 8^2 * 36 = 15360 * pi + 768 * pi = 16128 * pi. Using pi = 3.14, V = 50641.92. The provided answer 50688 assumes pi = 22/7.

AI explanation

The total volume is the sum of the cylindrical part and the conical part. Using the cylinder volume formula, we calculate pi * 8 * 8 * 240 to get 15360 * pi. Using the cone volume formula, we calculate 1/3 * pi * 8 * 8 * 36 to get 768 * pi. Adding these volumes gives 16128 * pi, and substituting 22/7 for pi gives a total volume of 50688 cubic centimeters.

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