Discussion
A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises (in cm) by
Answer: A
The submerged sphere displaces its own volume, which then spreads across the cylinder's cross-section.
\[ V_{\text{sphere}} = \frac{4}{3}\pi (9)^{3} = \frac{4}{3}\pi (729) = 972\pi \text{ cm}^{3} \]
\[ \text{cylinder cross-section} = \pi (18)^{2} = 324\pi \text{ cm}^{2} \]
\[ \text{rise} = \frac{972\pi}{324\pi} = 3 \text{ cm} \]
Both diameters must be halved before use; the \( \pi \) then cancels and no approximation is needed.
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