When an Oil Well Burns, Sediment Is Carried Up into the Air

question 26

Multiple Choice

When an oil well burns, sediment is carried up into the air by the flames and is eventually deposited on the ground.Less sediment is deposited further away from the oil well.Suppose that the density (in tons/square mile) at a distance r from the burning oil well is given by $\frac{9}{1+r^{2}}$ .Which Riemann sum approximates the total amount of sediment which is deposited within 100 miles of the well?

• A) \(\sum \frac{9 \pi r^{2} \Delta r}{1+r^{2}}\)
• B) \(\sum \frac{18 \pi r^{2} \Delta r}{1+r^{2}}\)
• C) \(\sum \frac{18 \pi r \Delta r}{1+r^{2}}\)
• D) \(\sum \frac{9 \pi r \Delta r}{1+r^{2}}\)

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Definitions:

U-joint Puller

A specialized tool used to remove universal joints (U-joints) from drive shafts without causing damage.

Driveshaft U-joints

Universal joints on a driveshaft that allow for changes in the angle of the transmission of power between components.

Propeller Shaft Assemblies

Components that transmit power from the vehicle's engine or transmission to the differential, allowing for motion in rear-wheel or four-wheel drive vehicles.

Engineered

The process of designing, constructing, and testing structures, materials, and systems based on scientific principles.