Calculate cuboid (rectangular prism) volume, total surface area, lateral area, and space diagonal from length, width, and height.
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A cuboid (or rectangular prism) is a convex polyhedron bounded by six rectangular faces. Opposite faces are congruent rectangles, meeting at right angles (90°).
V = lwh, \quad A_{\text{total}} = 2(lw + lh + wh), \quad d = \sqrt{l^2 + w^2 + h^2}Volume is the product of length, width, and height. Total surface area is the sum of the areas of the three pairs of opposing rectangular faces.
Scenario: Calculate cuboid with length l = 8 m, width w = 5 m, height h = 3 m
Volume: V = 8 × 5 × 3 = 120 m³
Surface Area: A = 2 × (8×5 + 8×3 + 5×3) = 2 × (40 + 24 + 15) = 2 × 79 = 158 m²
Lateral Area: A_lat = 2 × 3 × (8 + 5) = 6 × 13 = 78 m²
Space Diagonal: d = √(8² + 5² + 3²) = √(64 + 25 + 9) = √98 ≈ 9.8995 m
A cube is a special cuboid where length, width, and height are identical (all 6 faces are squares).
Apply 3D Pythagorean theorem: d = √(length² + width² + height²).
It is the area of the four side faces: A_lat = 2h(l + w), excluding the top and bottom faces.
A cuboid has 6 faces, 12 edges (4 lengths, 4 widths, 4 heights), and 8 vertices.
Calculate cube volume, total surface area, lateral surface area, space diagonal, and inradius from side length with step-by-step steps.
Calculate rectangle area, perimeter, diagonal, and aspect ratio from length and width with complete mathematical steps.
Calculate right circular cylinder volume, total surface area, lateral (curved) surface area, and base area from radius and height.