Home
Intriguing Intersections ★★★ Miss the Mark ★★★ Make Hundred ★★★ Long Division ★★★ Faites Vos Jeux ★★★ Men on the Moon ★★★ The King's Gold ★★★ Replacement Resistance ★★★ Angled Triangle ★★★ Tittle-Tattle ★★★ Elegant Equation ★★★ Pastor Petersen ★★★ Green Green Grass ★★★ Water Bucket ★★★Dog's Mead ★★★Troubling Twenty-Four ★★★Confusing Clock ★★★Spirited Soldier ★★★Melting Snowballs ★★★Friday the Thirteenth ★★★★ Leaning Ladder ★★★★
List of All PuzzlesAbout this SiteSend an E-mailPrivacy Policy

Solution to: Water Bucket

The surface of a cylinder with an open upper side is: O = π × R2 + 2 × π × R × H, where R is the radius of the cylinder and H is the height. The volume is given, V = 30 = π × R2 × H liters (or dm3). The surface can then be written as O = π × R2 + 2 × V/R. If you take the first derivative of R and look where this derivative equals 0 you get Rmin = (V/π)1/3. So the minimum surface is O = π × Rmin2 + 2 × π × Rmin × H = 3 × π1/3 × V2/3 or about 42.42 dm2.


Back to the puzzle
×