Faraday's First Law of Electrolysis:
Statement:
Faraday's first law of electrolysis states that the amount of a substance deposited or liberated at an electrode during electrolysis is directly proportional to the amount of electric charge passed through the electrolyte.
Mathematical Form:
The law can be expressed as:
\(m = \frac{M \cdot Q}{F \cdot z}\)
where: - \(m\) is the mass of the substance deposited or liberated, - \(M\) is the molar mass of the substance, - \(Q\) is the total charge passed through the electrolyte (in coulombs), - \(F\) is the Faraday constant (approximately 96500 C/mol), - \(z\) is the valency of the ion (the number of electrons involved in the reaction).Implication:
This law indicates that the amount of substance deposited or liberated at the electrodes is proportional to the total charge passed, making electrolysis a controlled method for determining the quantity of material involved in redox reactions. Faraday’s first law is fundamental to understanding electroplating, electrorefining, and the electrolysis of water and salts.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).