$\"\"$

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(a)

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The plate is circular with center $\"\"$ .

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The diameter of the plates is shown the figure is $\"\"$ .

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Radius is half of the diameter lenght.

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$\"\"$

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$\"\"$

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$\"\"$

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The standard form of circle is $\"\"$ .

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Consider $\"\"$ is $\"\"$ and the radius of the circle is $\"\"$ .

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Substitue $\"\"$ and $\"\"$ in standard equation of circle.

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The ellipse of circle is $\"\"$ .

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$\"\"$

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(b)

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The standard form of surface area of the circle is $\"\"$ .

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The diameter of the each cap is $\"\"$ .

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Radus of the cap is $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in area of the circle.

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$\"\"$

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$\"\"$

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Find the total area of the each bubble:

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Each bubble area is $\"\"$ .

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The total bubbles are $\"\"$ , Then are is $\"\"$ .

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Find the total area of the plate:

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Substitute $\"\"$ in the $\"\"$

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$\"\"$

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$\"\"$

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The surface area of the plates not covered by bubble caps.

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So,area=total area-total each bubble area.

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Substutute $\"\"$ and $\"\"$ in the not covered by bubble caps area.

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$\"\"$

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$\"\"$

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The surface area of the plates not covered by bubble caps is $\"\"$ .

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$\"\"$

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(a) The equation of the plate is $\"\"$ .

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(b) The surface area of the plates not covered by bubble caps is $\"\"$ .