answer:
To calculate the depth of water in the inverted cone, we can use the concept of similar triangles. Here's the step-by-step solution:
1. Let's denote the depth of water as "h" (measured from the vertex).
2. Since the cone is inverted, the water forms a smaller cone inside the larger cone.
3. The volume of a cone can be calculated using the formula V = (1/3) * π * r^2 * h, where "V" is the volume, "π" is pi (approximately 3.14159), "r" is the radius of the base, and "h" is the height.
4. In this case, the volume of water is given as 20 cm^3, so we have (1/3) * π * 6^2 * h = 20.
5. Simplifying the equation, we get 36π * h = 60.
6. Divide both sides of the equation by 36π to isolate "h". This gives us h = 60 / (36π).
7. Now, let's calculate the numerical value of h using a calculator. The approximate value of π is 3.14159, so h ≈ 60 / (36 * 3.14159).
8. Evaluating this expression, we find that h ≈ 0.5307 cm.
9. Therefore, the depth of the water in the cone, measured from the vertex, is approximately 0.5307 cm.
real