Math Problem Statement

A circular swimming pool has a diameter of 20 ft, the sides are 6 ft high, and the depth of the water is 5 ft. How much work (in ft-lb) is required to pump all of the water out over the side? (Use the fact that water weighs 62.5 lb/ft^3

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Work and Energy
Integration
Fluid Mechanics

Formulas

Work formula: W = ∫ ρ A(y) D(y) dy
Area of a circle: A(y) = πr²
Weight density of water: ρ = 62.5 lb/ft³
Distance to pump: D(y) = 6 - y

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

College level (Calculus-based physics or engineering)