False bottom

The optical illusion of a large yoghurt is presented by the dairy Z with its Greek yoghurt. The yoghurt has a kind of false bottom. From the outside it looks like a nice big one, and the yoghurt itself is in a smaller plastic container placed in a larger paper container. The net weight of course matches, but the customer unnecessarily pays for the false bottom - the extra paper container. Even when the yoghurts are stacked, they take up a larger volume, and the lorry carries unnecessarily extra air.

The yoghurt has the shape of a truncated cone, but for our calculations let us consider a cylinder with a diameter of 83 mm. The outer container has a depth of 49 mm. The inner container, which is the one that contains the yoghurt, has however a depth of only 37 mm.

Calculate by how many percent the volume of the outer container of the yoghurt is greater than the volume of the inner container (i.e. by how many percent the packaging of the yoghurt tries in the eyes of the customer to be larger than it actually is).

Final Answer:

p =  32.43 %

Step-by-step explanation:

$$\begin{gathered} d=49\text{mm} \\ {h}_1=49\text{mm} \\ {h}_2=37\text{mm} \\ V=\pi r^2\cdot h \\ p=100\cdot \frac{V_1-V_2}{V_2} \\ p=100\cdot \frac{\pi r^2{h}_1-\pi r^2{h}_2}{\pi r^2{h}_2} \\ p=100\cdot \frac{h_1-h_2}{h_2}=100\cdot \frac{49-37}{37}=32.43\% \end{gathered}$$

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