Final answer:
The volume of the larger cylinder is 2 times greater than the volume of the smaller cylinder.
Step-by-step explanation:
The volume of a cylinder is calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
For the first cylinder with a radius of 5cm and a height of 10cm, the volume is calculated as:
V₁ = 3.142 × (5 cm)² × 10 cm = 785.5 cm³
For the second cylinder with a radius of 5cm and a height of 20cm, the volume is calculated as:
V₂ = 3.142 × (5 cm)² × 20 cm = 1571 cm³
To find the relationship between the volumes, we can divide the volume of the larger cylinder by the volume of the smaller cylinder:
V₂ / V₁ = 1571 cm³ / 785.5 cm³ = 2
Therefore, the volume of the larger cylinder is 2 times greater than the volume of the smaller cylinder.