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EEJ MAIN Aptitude QUESTION #10993
Question 1
A solid consists of a hemisphere of radius $R$ surmounted by a right circular cone of the same base radius and height $h$. If the total volume equals the volume of a sphere of radius $R$, what is $h$?
  • $R$
  • $2R$✔️
  • $\frac{3R}{2}$
  • $\frac{4R}{3}$
Correct Answer Explanation
Volume of hemisphere: $\frac{2}{3}\pi R^3$. Volume of cone: $\frac{1}{3}\pi R^2 h$. Total = $\frac{4}{3}\pi R^3$ (sphere volume). So $\frac{2}{3}\pi R^3 + \frac{1}{3}\pi R^2 h = \frac{4}{3}\pi R^3$. Simplifying: $2R + h = 4R$, giving $h = 2R$.