Math Problem Statement

a circular swimming pool has a diameter of 8 m, the sides are 3 m high and the depth of the water is 2 m. The density of water is 1000 kg/m^3. Set up but do not evaluate an integral that represents the work required to pump all of the water out over the side.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Work-Energy Principle
Definite Integrals

Formulas

Work: W = ∫ (force) * (distance) dy
Volume of a slice: dV = A * dy = 16π dy
Weight: Weight = 156800π dy

Theorems

Work-Energy Theorem
Volume and Weight Calculation

Suitable Grade Level

Grades 11-12 (AP Calculus)