Use differentials to estimate the amount of paint needed to apply a coat of paint $0.0017 \mathrm {~cm}$ thick to a hemispherical dome with diameter $70 \mathrm {~m}$.
A) $4.165 \pi$
B) $2.52 \pi$
C) $4.11 \pi$
D) $3.82 \pi$
E) $2.28 \pi$

Question

Quizplus · Accepted Answer

The surface area of a hemisphere is $2\pi r^2$. With $r = 35 \, \text{m}$, the differential $dA = 2\pi r \cdot dr$ gives the change in area for a small thickness $dr = 0.0017 \, \text{cm} = 0.000017 \, \text{m}$. Calculating $dA$ gives $4.165 \pi$.

Use Differentials to Estimate the Amount of Paint Needed to Apply