Answer:
2√6 m
Explanation:
The formula for the vol. of a cone is V = (1/3)(area of base)(height).
Here, V = 20π m³ = (1/3)(area of the base)(10 m)
We need to solve for (area of the base).
Multiplying both sides of this equation by (3/10) results in:
(3/10)(20 π m³) = (area of the base)
This simplifies to 6π m² = (area of the base)
We still must find the diameter of the base. Let's find the radius of the base first: The formula for the area of a circle is A = πr². Here we have 6π m² = πr², which tells us that r² = 6 m². Since d = 2r, and r = d/2, r² = d²/4. Then the equation 6 m² = r² becomes:
6 m² = d²/4.
Solve this for d. Multiplying both sides by 4, we get:
24 m² = d²2, and d = √(24 m²) = 2√6 m
The cone diameter is 2√6 m.