Multiple choice

A solid is in the form of a right circular cone mounted on a solid hemisphere with same radius is made from a piece of metal. The radius of the hemisphere is $\displaystyle \frac{1}{3}$ of the vertical height of the conical part. If the radius of the base of the cone is r, the volume of the piece of metal is

  1. $\displaystyle \frac{11}{3}\pi\, r^{3}$
  2. $\displaystyle \frac{8}{3}\pi\, r^{3}$
  3. $\displaystyle \frac{7}{3}\pi\, r^{3}$
  4. $\displaystyle \frac{5}{3}\pi\, r^{3}$
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D Correct answer
Explanation

Radius of hemisphere = r. Height of cone = 3r. Volume = (2/3) * pi * r^3 (hemisphere) + (1/3) * pi * r^2 * (3r) (cone) = (2/3) * pi * r^3 + pi * r^3 = (5/3) * pi * r^3.

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