Question

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

Answer 1

Answer:

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.

Answer 2

Answer:

2√6 m

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