Law Of The Donut Math Answer Key -

[ V = (\pi r^2) \times (2\pi R) = 2\pi^2 R r^2 ] For surface area ( S ):

It sounds like you’re referring to the — a common playful name for a math problem involving torus volume or surface area , often found in calculus or geometry classes. Law Of The Donut Math Answer Key

Derivation: Perimeter of tube cross-section = ( 2\pi r ) Distance traveled by its centroid = ( 2\pi R ) Product = ( (2\pi r)(2\pi R) = 4\pi^2 R r ). Example 1: ( R = 5 ) cm, ( r = 1 ) cm [ V = 2\pi^2 (5)(1^2) = 10\pi^2 \ \text{cm}^3 ] [ S = 4\pi^2 (5)(1) = 20\pi^2 \ \text{cm}^2 ] [ V = (\pi r^2) \times (2\pi R)

[ V = 2\pi^2 R r^2 ]