Practice Problems

Grade 10 Sphere Volume Questions: Curriculum Standard Test Prep

Standardized 10th-grade geometry exam questions covering composite 3D solids and algebra transformations.
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📅 Updated: October 13, 2026
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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.

Sphere Volume Formula

Sphere Volume Formula

V = (4/3) × π × r³
Where V = Volume • r = Radius • π ≈ 3.14159265

Essential Mathematical Notation

  • V Volume of the sphere — The three-dimensional space enclosed within the spherical surface, measured in cubic units (e.g., cm³, m³, in³, ft³).
  • r Radius of the sphere — The straight-line distance from the exact center to any point on the outer surface (r = d / 2).
  • π Pi (π) — The mathematical circle constant, approximately 3.14159265 (or 22/7).
  • 4/3 Geometric Constant (4/3) — The rational coefficient derived from spherical calculus integration.
  • r³ Radius Cubed (r³) — The radius multiplied by itself three times (r × r × r), measuring 3D volume.
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