Discussion
2 cm thick 14 metal plates are kept exactly one above the other. On the top plate a hemisphere of diameter 6cm is kept. This just covers the top plate. What is the volume of the entire object?
Answer: D
The hemisphere of diameter 6 cm just covers the top plate, so each plate is a disc of radius 3 cm and thickness 2 cm.
\[ V_{\text{one plate}} = \pi r^{2} h = \pi (3)^{2}(2) = 18\pi \text{ cm}^{3} \]
\[ V_{\text{14 plates}} = 14 \times 18\pi = 252\pi \text{ cm}^{3} \]
\[ V_{\text{hemisphere}} = \frac{2}{3}\pi r^{3} = \frac{2}{3}\pi (27) = 18\pi \text{ cm}^{3} \]
\[ V_{\text{total}} = 252\pi + 18\pi = 270\pi \text{ cm}^{3} \]
"Just covers" is the clue that fixes the plates' radius at 3 cm - without it the plate dimensions would be unknown.
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