Final answer:
The volume of the cylindrical part of an architectural column is calculated using the formula V = πr²h. With a diameter of 20 cm (radius of 10 cm) and height 320 cm, the volume is 100,480 cm³.
Step-by-step explanation:
To find the volume of the cylindrical part of an architectural column, we will use the formula for the volume of a cylinder, which is V = πr²h. In this formula, r is the radius of the base of the cylinder, and h is the height. First, we need to remember to convert the diameter to a radius by dividing by two; thus, the radius r is 10 cm. Then, using 3.14 for π and the given height h of 320 cm, we calculate the volume as follows:
V = 3.14 × (10 cm)² × 320 cm
V = 3.14 × 100 cm² × 320 cm
V = 3.14 × 32,000 cm³
V = 100,480 cm³
So, the volume of the cylinder is 100,480 cm³, which rounded to the nearest cubic centimeter as requested, is 100,480 cm³.