Final answer:
The exact volume of the cylinder with a 10 ft diameter and 8 ft height is found using the formula V = πr²h. With a diameter of 10 ft, the radius is 5 ft. The calculated volume is 628.318 cubic feet.
Step-by-step explanation:
To find the exact volume of a cylinder with a diameter of 10 ft and a height of 8 ft, we can use the following formula:
V = πr²h
Where V is the volume, r is the radius of the cylinder (half of the diameter), h is the height, and π (pi) is approximately 3.14159. Since the diameter is given as 10 ft, the radius will be 5 ft (half of the diameter).
Substituting our values into the formula gives us:
V = π × (5 ft)² × 8 ft
V = 3.14159 × 25 ft² × 8 ft
V = 3.14159 × 200 ft³
V = 628.318 ft³
Therefore, the exact volume of the cylinder is 628.318 cubic feet.