Math Problem Statement

A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 3 ft at the south end to 8 ft at the north end. Find the volume of water (in ft³) in the pool.

Solution

It appears that you have uploaded an image related to a math problem. This problem involves calculating the volume of water in a swimming pool.

From the text visible in the image, the swimming pool has a circular shape with a 20-foot diameter. The depth is constant along east-west lines, increasing from 3 feet at the south end to 8 feet at the north end. The task is to find the volume of water in the pool in cubic feet (ft³).

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Math Problem Analysis

Mathematical Concepts

Calculus
Volume calculation using double integrals
Linear functions

Formulas

Volume = ∬_R depth(x, y) dA, where R is the region of the circular pool
Equation of a line: depth = mx + c (for linear depth variation)

Theorems

Double integral for volume under a surface

Suitable Grade Level

College Level

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