Final answer:
The height of the vertex of the funnel above the bottom of the glass is 8.4 cm.
Step-by-step explanation:
To find the height of the vertex of the funnel above the bottom of the glass, we need to determine the height of the funnel and subtract it from the total height of the glass. The height of the funnel can be found using similar triangles.
First, we need to find the radius of the funnel by dividing the diameter by 2: 8.2 cm ÷ 2 = 4.1 cm. Next, we can use the similar triangles formed by the glass and the funnel to set up a proportion: Height of the funnel / 4.1 cm = Height of the glass / 12.5 cm.
Now, we can solve for the height of the funnel: Height of the funnel = (Height of the glass × 4.1 cm) / 12.5 cm. Plugging in the values, we get: Height of the funnel = (12.5 cm × 4.1 cm) / 12.5 cm = 4.1 cm. Finally, we can find the height of the vertex by subtracting the height of the funnel from the total height of the glass: Height of the vertex = Height of the glass - Height of the funnel = 12.5 cm - 4.1 cm = 8.4 cm.