Answer:
Approximately 5.988 inches
Step-by-Step Step-by-step explanation:
The formula for the volume of a cone is:
V = (1/3)πr^2h
where V is the volume, r is the radius of the base, h is the height, and π is the mathematical constant pi.
We are given that the volume of the cone is 37.7 cubic inches, and the height is 4 inches. We can plug these values into the formula and solve for the radius:
37.7 = (1/3)πr^2(4)
37.7 = (4/3)πr^2
r^2 = (37.7 x 3) / (4 x π)
r^2 = 8.9717
r ≈ 2.994 inches
Now that we know the radius of the base, we can find the diameter by doubling the radius:
d = 2r ≈ 5.988 inches
Therefore, the diameter of the base of the cone is approximately 5.988 inches.