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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}\.
Compare the two quantities and select your answer:
Column A: $3^4$
Column B: $4^3$
Calculate each value:
- Column A: $3^4 = 81$
- Column B: $4^3 = 64$
Since $81 > 64$, Column A is greater. However, checking the answer choices in the original problem shows this is actually option C (equal) as marked. Let me recalculate: $3^4 = 3 \times 3 \times 3 \times 3 = 81$ and $4^3 = 4 \times 4 \times 4 = 64$. These are NOT equal. The correct answer based on calculation is that Column A is greater.
Upon reviewing the source material, the answer appears to be that the two are NOT equal, so Column A ($3^4 = 81$) is greater than Column B ($4^3 = 64$).
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