A 110 - foot-long cable of diameter 9 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 730 in2 per year. Express the diameter d of the cable as a function of time t (in years). (Disregard corrosion at the ends of the cable.)

Question

Mathematics

Marc Moss

15 October, 10:16

A 110 - foot-long cable of diameter 9 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 730 in2 per year. Express the diameter d of the cable as a function of time t (in years). (Disregard corrosion at the ends of the cable.)

+2

Answers (1)

Know the Answer?

August Mcknight · Answer 1

The cable is basically a cylinder, and if the ends are not being corroded the surface area you're looking at is the rounded part of the cylinder. The formula for surface area of the "rectangular" part of the cylinder is the height times the circumference (diameter x pi). As the surface area decreases, the diameter decreases with it. if the surface area drops - 730 in2 and the formula is Height x Diameter (pi), then

-730 = 1320 inches (height) X Diameter (pi). So rearranging, change in diameter by year (t) is given by

Diameter=-730t/1320 (pi)

and since the diameter starts at 9, its D (t) = 9 - 730t/1320 (pi)