Calculate right circular cylinder volume, total surface area, lateral (curved) surface area, and base area from radius and height.
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A right circular cylinder is a three-dimensional solid formed by two congruent circular bases in parallel planes connected by a curved surface perpendicular to both bases.
V = \pi r^2 h, \quad A_{\text{lat}} = 2\pi r h, \quad A_{\text{total}} = 2\pi r(r + h)Volume equals base circular area (πr²) multiplied by height. Lateral area unrolls into a rectangle of width 2πr and height h.
Scenario: Find volume and surface area of a cylinder with radius r = 3 cm and height h = 10 cm
Base Area: A_base = π × 3² = 9π ≈ 28.2743 cm²
Volume: V = 9π × 10 = 90π ≈ 282.7433 cm³
Lateral Area: A_lat = 2 × π × 3 × 10 = 60π ≈ 188.4956 cm²
Total Surface Area: A_total = 2(28.2743) + 188.4956 ≈ 245.0442 cm²
The curved (lateral) surface area is 2πrh, representing only the outer cylinder wall without the circular top and bottom caps.
Radius is diameter / 2. Then V = π × (d/2)² × h = (π/4) × d² × h.
An oblique cylinder is one where the centers of the circular bases are not aligned perpendicularly. By Cavalieri’s principle, its volume is still V = πr²h.
Divide volume by base area: h = V / (πr²).
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