Question5. Marie-Claude has a series of four nested funnels in her kitchen that are similar to the one shown in the diagram. If the other three funnels have top diameters of $10 \mathrm{~cm}, 8 \mathrm{~cm}$, and 6 cm , find the measures of the remaining parts for all three funnels.

Studdy Solution
Calculate the diameter of the narrow tube for each funnel using the similarity ratio. The diameter of the narrow tube of the given funnel is 2 cm.
For the 10 cm funnel: $$\text{Diameter of Narrow Tube} = 2 \times \frac{5}{6} = \frac{10}{6} = 1.67 \, \text{cm}$$
For the 8 cm funnel: $$\text{Diameter of Narrow Tube} = 2 \times \frac{2}{3} = \frac{4}{3} = 1.33 \, \text{cm}$$
For the 6 cm funnel: $$\text{Diameter of Narrow Tube} = 2 \times \frac{1}{2} = 1 \, \text{cm}$$
The measures of the remaining parts for each funnel are as follows:
- For the 10 cm funnel: Total height = 13.33 cm, Height of conical part = 8.33 cm, Diameter of narrow tube = 1.67 cm. - For the 8 cm funnel: Total height = 10.67 cm, Height of conical part = 6.67 cm, Diameter of narrow tube = 1.33 cm. - For the 6 cm funnel: Total height = 8 cm, Height of conical part = 5 cm, Diameter of narrow tube = 1 cm.