A boundary stripe 2 in. wide is painted around a rectangle whose dimensions are $100 \mathrm { ft }$ by $240 \mathrm { ft }$. Use differentials to approximate the number of square feet of paint in the stripe.
A) $\quad 113 \mathrm { ft } ^ { 2 }$
B) $\quad 113.81 \mathrm { ft } ^ { 2 }$
C) $\quad 113.22 \mathrm { ft } ^ { 2 }$
D) $\quad 113.89 \mathrm {} \mathrm { tt } ^ { 2 }$
E) $\quad 113.33 \mathrm { ft } ^ { 2 }$

Question

Quizplus · Accepted Answer

The differential of the area $dA$ is approximately $2(l + w) \cdot dw$, where $l = 240$ ft, $w = 100$ ft, and $dw = \frac{2}{12}$ ft. Calculating gives $dA \approx 2(240 + 100) \cdot \frac{2}{12} = 113.33$ ft².

A Boundary Stripe 2 In 100ft100 \mathrm { ft }100ft By 240ft240 \mathrm { ft }240ft

A Boundary Stripe 2 In $100 \mathrm { ft }$ By $240 \mathrm { ft }$