2026-09-10T00:15:04.002847 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL Calculate the capacity of the larger of two mathe...
Question 1 Report
Calculate the capacity of the larger of two mathematically similar bottles. The diagram shows the two bottles.
The smaller bottle is \(15\) cm high and holds \(540\) ml, and the larger bottle is \(20\) cm high. Give your answer in millilitres.
Answer Details
For similar three-dimensional objects, capacities and volumes scale by the cube of the length scale factor.
\[\text{length scale factor}=\frac{20}{15}=\frac{4}{3}\]
[M1]
\[\text{volume scale factor}=\left(\frac{4}{3}\right)^3=\frac{64}{27}\]
[M1 A1]
\[\text{larger capacity}=540\times\frac{64}{27}=20\times64=1280\text{ ml}\]
[A1] The larger bottle holds \(1280\text{ ml}\).
Use a cube for capacity because capacity measures three-dimensional space.
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