Discussion
A hemisphere is made of a sheet of a metal 1 cm thick. If the outer radius is 5 cm, what is the weight of the hemisphere (1 cm³ of the metal weigh 9 g)?
Answer: B
The sheet is 1 cm thick, so the outer radius is 5 cm and the inner 4 cm. The metal is the shell between them.
\[ V = \frac{2}{3}\pi\left(R^{3} - r^{3}\right) = \frac{2}{3}\pi(125 - 64) \]
\[ = \frac{2}{3}\pi(61) = \frac{122\pi}{3} \text{ cm}^{3} \]
\[ \text{weight} = \frac{122\pi}{3} \times 9 = 366\pi \text{ g} \]
Treating the hemisphere as solid would give \( \tfrac{2}{3}\pi(125) \times 9 = 750\pi \) g - the cavity must be subtracted.
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