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In-depth guides on formulas, worked examples, and practical methods for maths, packaging, finance, and fitness problems.

Three layers of spheres inside a cylinder with radius R and height H labelled

June 17, 2026·10 min read

Sphere Packing in a Cylinder: How to Calculate the Optimal Radius and Height

Use the radius ratio table to find spheres per layer, then divide height by diameter to count layers. Worked examples for r = 7.5 h = 14.5, r = 10 h = 11, and more.

Sphere Packing

June 15, 2026·8 min read

How to Find the Optimal Box Dimensions to Pack 27 Spheres

The optimal box for 27 spheres of radius 2 cm is a 12 × 12 × 12 cm cube. Learn the formula, step-by-step method, surface area calculations, and worked examples for any sphere count or box size.

Sphere Packing