SSGM6

3-D Mensuration II — Spheres

Calculate surface area and volume of spheres and hemispheres; apply to real-life contexts.

The Sphere — Properties and Surface Area

Volume of a SphereComplete the earlier lesson to unlock

The Hemisphere — Surface Area and VolumeComplete the earlier lesson to unlock

Reverse Problems and the Equal-ConditionComplete the earlier lesson to unlock

Composite Solids, Recast Problems, and Real-Life ApplicationsComplete the earlier lesson to unlock

Unit review reward

All 5 lessons in 3-D Mensuration II — Spheres

1. The Sphere — Properties and Surface Area

Define a sphere and its great circle, derive SA = 4 pi r^2, and apply it, converting diameter to radius first.

2. Volume of a Sphere

Derive and apply V = 4/3 pi r^3 using the Archimedes ratio, convert diameter to radius, find r from V, and use conservation of volume.

3. The Hemisphere — Surface Area and Volume

Define a hemisphere; derive and apply CSA = 2 pi r^2, TSA = 3 pi r^2, and V = 2/3 pi r^3; distinguish a solid hemisphere from an open bowl.

4. Reverse Problems and the Equal-Condition

Rearrange sphere and hemisphere formulas to find the radius; chain volume to surface area; solve the equal-condition and surface-area-change problems.

5. Composite Solids, Recast Problems, and Real-Life Applications

Identify external vs seam surfaces; find TSA and volume of cylinder+hemisphere and cone+hemisphere solids; solve recast and capacity problems by conservation of volume.

Unit code SSGM6