The volume of a cone with a height of 10 meters is 20 pi cubic meters. what is the diameter of the cone?

2√6 m

Step-by-step explanation:its right just did test

2√6 m

Step-by-step 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.