Question

the volume of a cylinder is given by the formula ( v=pi r^{2} h ), where ( r ) is the radius of the c which expression represents the volume of this cylinder? ( h = 2 x + 7 ) ( r = x - 3 ) ( 2 pi x^{3}-12 pi x^{2}-24 pi x + 83 pi ) ( 2 pi x^{3}-5 pi x^{2}-24 pi x + 63 pi ) ( 2 pi x^{3}+7 pi x^{2}-18 pi x - 63 pi )

Explanation:

Step1: Substitute \(r = x - 3\) and \(h=2x + 7\) into \(V=\pi r^{2}h\)

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Step2: Expand \((x - 3)^{2}\)

Using the formula \((a - b)^{2}=a^{2}-2ab + b^{2}\), where \(a = x\) and \(b = 3\), we get \((x - 3)^{2}=x^{2}-6x + 9\)

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Step3: Multiply \((x^{2}-6x + 9)\) by \((2x + 7)\)

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Step4: Multiply by \(\pi\)

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Answer:

\(2\pi x^{3}-5\pi x^{2}-24\pi x + 63\pi\) (the second option)