Final answer:
To calculate the volume of the finished cylinder with a hole, subtract the volume of the hole from the volume of the original cylinder, resulting in a final volume of 918π cm³.
Step-by-step explanation:
The volume of the original cylinder is given by the formula V = πr²h, where r is the radius of the cylinder and h is the height. To find the volume of the finished cylinder after the 14 cm diameter hole is made, we need to subtract the volume of the removed cylinder (the hole) from the volume of the original cylinder. Since the diameter of the hole is 14 cm, its radius is 7 cm. The radius of the original cylinder is 10 cm as its diameter is 20 cm. Using the volume formula, the volume of the original cylinder is V = π(10 cm)²(18 cm) = 1800π cm³. The volume of the hole is V = π(7 cm)²(18 cm) = 882π cm³. To find the final volume of the finished cylinder, we subtract the volume of the hole from the volume of the original cylinder: 1800π cm³ - 882π cm³ = 918π cm³.