Multiple choice

A solid is in the form of a cone of vertical height $9 cm$ mounted on the top base of a right circular cylinder of height $40 cm$. The radius of the base of the cone and that of the cylinder are both equal to $7 cm$. Find the weight of the solid if $1\, cm^{3}$ of the solid weighs $4 gm.$

  1. $26.488 kg$
  2. $25.488 kg$
  3. $24.488 kg$
  4. $23.488 kg$
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A Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = (22/7) * 7 * 7 * 40 = 6160 cm^3. Volume of cone = (1/3) * pi * r^2 * h = (1/3) * (22/7) * 7 * 7 * 9 = 462 cm^3. Total volume = 6622 cm^3. Weight = 6622 * 4 = 26488 gm = 26.488 kg.

AI explanation

The total volume is the sum of the cylinder volume, pi times r squared times h, and the cone volume, one third times pi times r squared times h. Substituting r = 7 cm, cylinder height = 40 cm and cone height = 9 cm gives a cylinder volume of 6160 cubic centimeters and a cone volume of 462 cubic centimeters, for a total of 6622 cubic centimeters. Multiplying 6622 by 4 gm gives 26488 gm, which equals 26.488 kg.

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