Final answer:
The volume of a cylinder with a radius of 4 units and a height of 12 units is greater than the volume of a rectangular prism with dimensions 8 units x 8 units x 6 units.
Step-by-step explanation:
To compare the volume of a cylinder with the volume of a rectangular prism, we can use the formulas for each shape. The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. Substituting the given values (r = 4 and h = 12) into the formula gives V = 3.142 × (4)² × 12 = 602.112 units³.
The volume of a rectangular prism is given by V = lwh, where l, w, and h are the dimensions. Substituting the given values (l = 8, w = 8, and h = 6) into the formula gives V = 8 × 8 × 6 = 384 units³.
Therefore, the volume of the cylinder (602.112 units³) is greater than the volume of the rectangular prism (384 units³). So, the correct answer is a) The cylinder's volume is greater.