Approximating changes. Approximate the amount of paint needed to apply a coat of paint $0\mathrm{.}05$ cm thick to a hemispherical dome with diameter $50$ m $.$ Use linear approximations. Also compute the exact amount of paint needed and compare to the linear approximation.

$]=\frac{0\mathrm{.}05}{100}=0\mathrm{.}0005m]=\frac{3}{2}*3r^{2}dr[2r^{2}dr[0\mathrm{.}0005m$

$dv=2*{25}^2*0\mathrm{.}0005$