Farmer bob\'s square plot ofland is slowly eroding away. Worried about the futur

Question

Farmer bob's square plot ofland is slowly eroding away. Worried about the future of his farm. Farmer Bob measures the rate of erosion and finds that the length of each side of his square plot is decreasing at the constant rate of 2 feet/year. If he currently owns 250,000 square feet of land, what is the current rate of change of the area of Farmer Bob's land?

a) Farmer bob is losing 2,000 square feet of land per year

b) losing 1,000,000 square feet of land per year

c) losing 1,000 square feet of land per year

d) losing 4 square feet of land per year

Explanation / Answer

a area A=L2,

length L =(250000)1/2=500

differentiating w.r.t to time t

dA/dt=2*LdL/dt=2*500*2=2000

hence option A

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