Two mathematically similar conical flasks, kept side by side on a shelf in a school science lab preparation room, have heights 8 cm and 20 cm. The smaller f...
Question 1 Report
Two mathematically similar conical flasks, kept side by side on a shelf in a school science lab preparation room, have heights 8 cm and 20 cm. The smaller flask has a capacity of 32 ml.
Work out the capacity of the larger flask. (3)
Answer Details
For similar solids, capacity (a volume) scales with the cube of the linear scale factor between corresponding lengths such as height.
Using the two heights, which are corresponding lengths:
\[\text{scale factor}=20\div8=2.5\] [1 mark]Capacity is 3-dimensional, so it scales with the cube of this linear factor:
\[\text{volume scale factor}=2.5^{3}=15.625\] [1 mark]Applying this to the smaller flask's capacity:
\[32\times15.625=500 \text{ ml}\] [1 mark]The height ratio, 2.5, describes how the flasks compare in one dimension only; because capacity depends on all three dimensions at once, it grows much faster than height, which is why the larger flask holds more than 15 times as much rather than only 2.5 times as much.
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