Explanation:
We can use the formula for the volume of a right circular cone, which 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 constant pi.
We are given that the volume of the cone is 162 cubic inches and the height is 6 inches, so we can substitute these values into the formula and solve for the radius:
162 = (1/3)πr^2(6)
Simplifying:
54 = πr^2
Dividing both sides by π:
r^2 = 54/π
Taking the square root of both sides:
r = sqrt(54/π) ≈ 4.115
Therefore, the radius of the base of the cone is approximately 4.115 inches.
To find the diameter of the base, we can multiply the radius by 2:
d = 2r ≈ 8.23
Therefore, the diameter of the base of the cone is approximately 8.23 inches.