Final answer:
To find the volume of sand in a cylinder with a 3 cm radius forming a 2 cm deep layer, the formula V = πr²h is used. The volume is calculated as π * (3 cm)² * (2 cm), resulting in 56.52 cm³.
Step-by-step explanation:
The question involves finding the volume of sand in a cylinder. To calculate the volume of the sand that forms a layer 2 cm deep in a cylinder that has a radius of 3 cm, we use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height (or depth).
Using the given radius (3 cm) and the depth of the sand layer (2 cm), the volume of the sand is calculated as follows:
- V = π * (3 cm)² * (2 cm)
- V = 3.14159 * 9 cm² * 2 cm
- V = 3.14159 * 18 cm³
- V = 56.52 cm³
So, the correct volume of the sand in the cylinder is 56.52 cm³, which corresponds to option (b).