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

Accepted Solution

Answer:2√6 mStep-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.