To find the number of spherical balls that can be made from a cylinder, we need to calculate the volume of the cylinder and the volume of each spherical ball, and then divide the volume of the cylinder by the volume of each spherical ball.

Given:
Height of the cylinder = 8 cm
Diameter of the cylinder = 14 cm

1. Calculating the volume of the cylinder:
The formula to calculate the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
Given the diameter of the cylinder = 14 cm, we can find the radius by dividing the diameter by 2.
Radius of the cylinder (r) = 14 cm / 2 = 7 cm

Now, we can calculate the volume of the cylinder using the formula:
Volume of the cylinder = π * (7 cm)² * 8 cm
Volume of the cylinder = 22/7 * 49 cm² * 8 cm
Volume of the cylinder = 1232 cm³

2. Calculating the volume of each spherical ball:
The formula to calculate the volume of a sphere is V = (4/3)πr³, where r is the radius.
Given the radius of the spherical ball = 1 cm

Now, we can calculate the volume of each spherical ball using the formula:
Volume of each spherical ball = (4/3) * 22/7 * (1 cm)³
Volume of each spherical ball = (4/3) * 22/7 * 1 cm³
Volume of each spherical ball = 4.19 cm³

3. Finding the number of spherical balls:
To find the number of spherical balls that can be made, we need to divide the volume of the cylinder by the volume of each spherical ball:
Number of spherical balls = Volume of the cylinder / Volume of each spherical ball
Number of spherical balls = 1232 cm³ / 4.19 cm³
Number of spherical balls ≈ 294.04

Since we cannot have a fraction of a ball, we round down the number to the nearest whole number.
Therefore, the number of spherical balls that can be made from the given cylinder is 294.

Hence, the correct answer is option B) 294.