How do I use linear approximation to find paint in cubic meters?

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.070000 cm thick to a hemispherical dome with a diameter of 30.000 meters. How do I do this?

An approximation is to find the surface area of the dome and multiply it by the thickness fo the paint

This is effectively making the dome flat, and making the paint into a rectangular prism, and finding the volume of that

The surface area of a sphere is 4 * pi * radius^2
so the surface area of the dome is 1/2 of that
= 2 * pi * radius^2

so the surface area of this dome will be
2 * pi * (30/2)^2
= 2 * pi * 225
= 450 * pi m^2

multiply this by the thickness of the paint (in metres) to find the volume of paint needed

The thickness of the paint is 0.07 cm = 0.0007 m (check this by working it out if you want to)

volume of paint needed =
450 * pi * 0.0007
=0.9896 m^3

or about 0.99 m^3

The actual volume of paint required can be found by finding the volume of the hemisphere, and the volume of the hemisphere with the paint, and taking one away from the other

You dont say whether the paint is on the outside or the inside
so i will do both:

1) The paint is on the outside of the hemisphere
We have to take the volume of the hemisphere from the volume of the hemisphere + paint

formula for volume of sphere = 4/3 * pi * radius^3

volume of hemisphere = 1/2 * 4/3 * pi * radius^3
=1/2 * 4/3 * pi * 15^3
= 2250 pi

volume of hemisphere + paint = 1/2 * 4/3 * pi * (radius + thickness of paint)^3
=1/2 * 4/3 * pi * (15+0.0007)^3
= 2250.315 pi

so the volume of the paint is
2250.315 pi - 2250 pi = 0.315 pi
= 0.9896 m^3 (again)

2) the paint is on the inside of the hemisphere
we want to take the volume of the hemisphere - paint
from the volume of the hemisphere

volume of hemisphere = 2250 pi

volume of hemisphere - paint =
1/2 * 4/3 * pi * (radius - thickness of paint)^3
= 1/2 * 4/3 * pi * (15-0.0007)^3
= 2249.685 pi

so the volume of paint is
2250 pi - 2249.685 pi = 0.315 pi
=0.9896 m^3

so you can see that a linear approximation works well in this case because the thickness of the paint is very small compared to the radius of the dome.

All of the 0.9896 m^3 results were different at lots of decimal places, but for any practical use, the volume required is about the same.

How many square meters of cement wall can 1 liter of white paint cover?

I want to validate the cost given by my neighbor who want to paint my unit but I do not know if the cost of labor and materials he indicated is correct so I want to know how many liters of paint is needed to paint my unit. Thank you.

One litre covers about 10-12 square meters. You might need three coats if you are not using plaster primer. So that will be 3-4 square metres or less.

It is a good suggestion to paint it yourself. I have painted many things and it really isn't that difficult.

National Grid- gas&electric meters-and my water meter-just wondering if I am allowed to paint them? National Grid- gas&electric meters-and my water meter-just wondering if I am allowed to paint them?

Regulations differ around the world.
Many times certain colors are dedicated to certain applications. E.g. red = hot water, blue = cold water, yellow = gas. If you start re-painting the meters, you might get into trouble. If your meters have the basic material color, e.g. brass, plastic, then I don't see much of a problem repainting them.
Attention: some countries the meters are not your property, they stay property of the provider. In that case you should ask.

How many square meters or centimeters can one gallon of paint cover?

Thanks so much!

Usually a gallon covers about 350 sqft - pls convert