Correct Answer: Option A

Explanation

Volume of cylinder = \(\pi\)r\(^2\)h = \(\pi\)a\(^2\)y

Volume of cone = \(\frac{1}{3}\) \(\pi\)r\(^2\)h =  \(\frac{1}{3}\) \(\pi\)a\(^2\)x

Total Volume = \(\pi\)a\(^2\)y +  \(\frac{1}{3}\) \(\pi\)a\(^2\)x  = \(\frac{3\pi a^2y + \pi a^2x}{3}\)

                        = \(\frac{\pi a^2}{3}(x + 3y)\)

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