Composite 3D Solids for 10th Grade
In Grade 10 geometry, exam problems rarely involve isolated spheres. They frequently test composite shapes, such as a cylinder capped with two hemispheres (a capsule).
Capsule Example Problem
A medication capsule has cylindrical body length h = 10 mm and hemispherical ends with radius r = 3 mm. Find its total volume.
1. The two hemispherical ends combine to form one complete sphere: V_sphere = 4/3 × π × 3³ = 36π mm³.
2. The cylinder volume: V_cylinder = π × r² × h = π × 3² × 10 = 90π mm³.
3. Total volume: V_total = 36π + 90π = 126π ≈ 395.84 mm³.