Geometry

Question Analysis:
This question involves calculating the combined volume of two solids: a cylinder and a hemisphere.
The focus is on correctly applying volume formulas and adding the results.

Key Concept Explanation:
Volume of a cylinder = π × r² × h
Volume of a hemisphere = (1/2) × (4/3)π × r³ = (2/3)π × r³

Step-by-Step Solution:
Given:
Radius (r) = 4 cm
Cylinder height (h) = 10 cm
Cylinder volume:
= π × 4² × 10 = π × 16 × 10 = 160π cm³
Hemisphere volume:
= (2/3)π × 4³ = (2/3)π × 64 = (128/3)π cm³
Total volume:
= 160π + (128/3)π
= (480/3 + 128/3)π = (608/3)π c...