Diameter of the hemispherical dome is m.

Radius of the sphere is m.

Thickness of the paint is cm.

Change in the radius is thickness of the coat m.

Volume of the hemisphere is half of the sphere

.

Change in volume results surface area of the hemisphere which represents the amount of paint to be required.

Apply derivative on each side.

.

Substitute and in the above expression.

Volume of the paint is .

The amount of paint to be required is .