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EEJ MAIN Aptitude QUESTION #10942
Question 1
A cone of radius 6 cm and height 8 cm is placed inside a cylinder of the same base radius and height. What fraction of the cylinder's volume is NOT occupied by the cone?
  • \(\dfrac{1}{3}\
  • \(\dfrac{2}{3}\✔️
  • \(\dfrac{3}{4}\
  • \(\dfrac{1}{4}\
Correct Answer Explanation

Volume of cylinder = \(\pi r^2 h = \pi \times 36 \times 8 = 288\pi\

Volume of cone = \(\dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 288\pi = 96\pi\

Volume NOT occupied = \(288\pi - 96\pi = 192\pi\

Fraction = \(\dfrac{192\pi}{288\pi} = \dfrac{2}{3}\

This confirms the classic result: a cone always occupies exactly \(\dfrac{1}{3}\ of the enclosing cylinder, so the remaining fraction is \(\dfrac{2}{3}\.