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Inga [223]
2 years ago
12

Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.04 cm thick to a hemispherical dome

with a of diameter 52 m
Mathematics
1 answer:
pogonyaev2 years ago
3 0

The amount of paint is the volume of paint needed.

The amount of paint needed is 0.065312 cubic meters

<h3>How to determine the amount of paint needed</h3>

The volume of a hemisphere is:

V = \frac 23\pi r^3

Differentiate the above equation

V' = 2\pi r^2 r'

The above equation represents the estimate of the amount of paint needed.

Where:

  • r represents the radius (r = 52/2 m)
  • r' represents the thickness (r' = 0.04 cm)

So, we have:

V' = 2\pi r^2 r'

V' = 2 * 3.14 * (52/2\ m)^2 * (0.04cm)

V' = 2 * 3.14 * (26\ m)^2 * (0.04cm)

Express cm as m

V' = 2 * 3.14 * (26\ m)^2 * (0.0004m)

V' = 0.065312 m^3

Hence, the amount of paint needed is 0.065312 cubic meters

Read more about volumes at:

brainly.com/question/10171109

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