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 $70 \mathrm {~m}$.
Select the correct answer.
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 a diameter of 70 m, the radius $r$ is 35 m. The differential $dV$ for the volume of paint is $dV = 2\pi r \cdot dr \cdot r = 2\pi r^2 \cdot dr$. Substituting $r = 35$ m and $dr = 0.0017$ cm = 0.000017 m, we get $dV = 2\pi (35)^2 \cdot 0.000017 = 4.165 \pi$.

Use Differentials to Estimate the Amount of Paint Needed to Apply