Suppose a rectangular parking lot is being constructed with

Suppose a rectangular parking lot is being constructed with concrete surface 50 meters by 80 meters. Suppose further that plastic trim is being placed around the concrete, and this plastic trim is 2 centimeters wide on the short side and 3 centimeters wide on the long side (the trim is the shaded part in the figure below).

(a) Find the exact (upward-facing) surface area of the trim, by computing the area difference of two rectangles, using your calculator.

(b) Estimate the (upward-facing) surface are of the trim using differentials. Give your in square meters to 3 places past the decimal.

Solution

let dimmension of parking lot are x , y

rectangular parking lot is being constructed with concrete surface 50 meters by 80 meters

x=50, y=80

plastic trim is 2 centimeters wide on the short side and 3 centimeters wide on the long side

(a)

exact surface area of the trim=[(50+2*(3_/100))*(80+2*(2_/100))] -(50*80)

exact surface area of the trim=[(50.06)*(80.04)] -(50*80)

exact surface area of the trim=6.8024 squaremeters

(b)

x=50,y=80,dx=2*0.03=0.06 ,dy=2*0.02=0.04

area of parking lot ,A=xy

differential:

dA=(dx *y)+(x *dy)

area of trim =dA

area of trim=(0.06*80)+(50*0.04)

area of trim=6.800 square meters