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anastassius [24]
3 years ago
11

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with dia

meter 42 m. (Round your answer to two decimal places.) m3
Mathematics
1 answer:
Tamiku [17]3 years ago
4 0

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.

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