Final answer:
To find the radius of a cone with a volume of 425 cubic yards and height of 10 yards, we use the volume formula for a cone, substitute the given values, simplify, and solve for the radius, which is approximately 6.4 yards.
Step-by-step explanation:
The question is asking us to find the radius of a cone given that the volume of a cone is 425 cubic yards and the height is 10 yards. The formula for the volume of a cone is: V = 1/3 πr²h, where V is the volume, r is the radius, and h is the height. Substituting the known values, we get: 425 = 1/3 πr²(10). Solving for r, we first multiply both sides by 3 to get rid of the fraction, giving us 1275 = πr²(10), and then divide both sides by 10π, yielding r² = 1275 / (10π). Taking the square root of both sides to solve for r, we find the radius of the cone. After calculating, the radius is approximately 6.4 yards.