Explanation:
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, h is the height, and π is the mathematical constant pi (approximately 3.14159).
In this case, we are given the volume V = 769.3 cubic millimeters and the height h = 15 mm. We can substitute these values into the formula and solve for the radius r:
V = (1/3)πr^2h
769.3 = (1/3)πr^2(15) // substitute V and h
769.3 = 5πr^2 // simplify
r^2 = 769.3/(5π) // divide both sides by 5π
r = √(769.3/(5π)) // take the square root of both sides
Using a calculator, we can evaluate the expression under the square root to get:
r ≈ 5.0
So the radius of the cone is approximately 5.0 millimeters.