Discussion
What is the weight of water contained in a conical vessel which is 21 cm deep and 16 cm in diameter?
Answer: D
The water weighs 1.408 kg.
The cone has radius 8 cm and height 21 cm. With \(\pi = \frac{22}{7}\):
\[ \begin{aligned} V &= \tfrac{1}{3}\pi r^{2} h \\ &= \tfrac{1}{3} \times \tfrac{22}{7} \times 64 \times 21 \\ &= 1408\ \text{cm}^{3} \end{aligned} \]
Water has a density of 1 g/cm3, so 1408 cm3 weighs 1408 g = 1.408 kg.
Using the diameter 16 cm as the radius gives four times as much. Leaving out the \(\frac{1}{3}\) gives 4.224 kg, the volume of a cylinder. Neither matches 2.480 kg or 3.875 kg, which do not follow from the dimensions.
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