Methods2023 Exam 2 Section A · Q17CAS active1 mark

Volume of a cylinder formed from a metal sheet

A rectangle of length x and width y. Two vertical dashed lines mark off a shaded central rectangle of width h (the cylinder's curved surface); in each of the two end strips is a shaded dashed circle of radius r touching the sides of the strip.

A cylinder of height $h$ and radius $r$ is formed from a thin rectangular sheet of metal of length $x$ and width $y$ , by cutting along the dashed lines shown below.

The volume of the cylinder, in terms of $x$ and $y$ , is given by

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\pi x^2 y

\dfrac{\pi xy^2 - 2y^3}{4\pi^2}

\dfrac{2y^3 - \pi xy^2}{4\pi^2}

\dfrac{\pi xy - 2y^2}{2\pi}

\dfrac{2y^2 - \pi xy}{2\pi}

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