Final answer:
Using the formulas for calculating volume, the cylinder's volume is 251.2 cubic inches, while the cone's volume, given its dimensions, is one-third of that. Thus, the volume of the cylinder is greater than that of the cone.
Step-by-step explanation:
The question asks us to compare the volume of a cylinder with the volume of a cone that have the same diameter of 8 inches. The cylinder's height is 5 inches, while the cone's height is 15 inches. The formula to calculate the volume of a cylinder is V = πr²h, where π is pi (3.14), r is the radius, and h is the height. The formula to calculate the volume of a cone is V = ρ (πr²h), where ρ is one-third.
First, we calculate the volume of the cylinder:
V = π × (8/2)� × 5
= 3.14 × 4² × 5
= 3.14 × 16 × 5
= 251.2 cubic inches.
Next, we calculate the volume of the cone:
V = 1/3 π × (8/2)� × 15
= 1/3 × 3.14 × 4² × 15
= 1/3 × 3.14 × 16 × 15
= 251.2 cubic inches.
Comparing these volumes, we see that the volume of the cylinder is exactly three times the volume of the cone because the cone's formula includes the term 1/3. Therefore, the correct answer is (a), the volume of the cylinder is greater than the volume of the cone.