Answered

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

Answer :

MRROYALGO

The amount of paint is the volume of paint needed.

The amount of paint needed is 0.065312 cubic meters

How to determine the amount of paint needed

The volume of a hemisphere is:

[tex]V = \frac 23\pi r^3[/tex]

Differentiate the above equation

[tex]V' = 2\pi r^2 r'[/tex]

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:

[tex]V' = 2\pi r^2 r'[/tex]

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

[tex]V' = 2 * 3.14 * (26\ m)^2 * (0.04cm)[/tex]

Express cm as m

[tex]V' = 2 * 3.14 * (26\ m)^2 * (0.0004m)[/tex]

[tex]V' = 0.065312 m^3[/tex]

Hence, the amount of paint needed is 0.065312 cubic meters

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