A boundary stripe 2 in. wide is painted around a rectangle whose dimensions are 100 ft by 240 ft. Use differentials to approximate the number of square feet of paint in the stripe.
A) 113 $\mathrm { ft } ^ { 2 }$
B) 113.81 $\mathrm { ft } ^ { 2 }$
C) 113.23 $\mathrm { ft } ^ { 2 }$
D) 113.89 $\mathrm { ft } ^ { 2 }$
E) 113.33 $\mathrm { ft } ^ { 2 }$

Question

Quizplus · Accepted Answer

The differential of area $dA$ is approximately $2(l + w) \cdot dw$, where $l$ and $w$ are the length and width of the rectangle, and $dw$ is the width of the stripe. Converting 2 inches to feet gives $dw = \frac{1}{6}$ ft. So, $dA \approx 2(100 + 240) \cdot \frac{1}{6} = 113.33 \, \mathrm{ft}^2$.

A Boundary Stripe 2 In ft2\mathrm { ft } ^ { 2 }ft2

A Boundary Stripe 2 In $\mathrm { ft } ^ { 2 }$