Geometry Area & Volume Calculator

Calculate area, perimeter, circumference, and volume for various geometric shapes with step-by-step mathematical breakdowns.

Cylinder volume mode defaults to radius and height so you can verify V = pi x r² x h and surface-area steps on the same page.

Calculated Dimensions

Volume942.4778
Base Area78.5398
Total Surface Area534.0708

Solving Formulas & Steps:

Base Area (Ab) = π × r² = π × 5² ≈ 78.5398
Volume (V) = Ab × h = 78.5398 × 12 ≈ 942.4778
Lateral Area (Al) = 2 × π × r × h = 2 × π × 5 × 12 ≈ 376.9911
Total Surface Area (At) = 2 × π × r × (r + h) = 2 × π × 5 × (5 + 12) ≈ 534.0708

Frequently Asked Questions

What is the formula for the volume of a cylinder?

The volume of a cylinder is computed as V = π × r² × h, where r is the radius of the circular base and h is the height of the cylinder.

How does the circumference of a circle relate to its area?

Both depend on the radius. Circumference is C = 2πr, while Area is A = πr². If you double the radius, the circumference doubles, but the area quadruples (2² = 4).