Question

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with diameter 42 m. (Round your answer to two decimal places.) m3

Answer 1

Step-by-step explanation:

The volume of a hemisphere is given by :

$V=\dfrac{2}{3}\pi r^3$

Taking differentiation,

$\dfrac{dV}{dr}=2\pi r^2$

So,

$dV=2\pi r^2\times dr$

Put r = 21 m and dr = 0.03 cm = 0.0003 m

$dV=2\pi \times 21^2\times 0.0003\\\\dV=0.831\ m^3$

Hence, this is the required solution.