Math Problem Statement
An explosion at an oil rig in the ocean causes an elliptical oil slick to spread on the surface of the water. The slick is a constant 7 inches thick. After several days, when the major axis of the slick is 8 miles long and the minor axis is 0.2 miles wide, it is determined that its length is increasing at the rate of 40 feet per hour, and its width is increasing at the rate of 4 feet per hour. At what rate (in cubic feet per hour) is oil flowing from the site of the rig at that time?
Oil is flowing at cubic feet per hour
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Rate of Change
Volume of Elliptical Cylinder
Unit Conversion
Formulas
Volume of an elliptical cylinder: V = (π × a × b × thickness) / 48
Rate of change of volume: dV/dt = (π × 7 / 48) × (a × db/dt + b × da/dt)
Theorems
Product Rule for Differentiation
Suitable Grade Level
Grades 11-12 (Advanced Calculus)
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