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Sagot :
From geometry, we know that:
• the volume of a sphere of radius r is:
[tex]V_S=\frac{4}{3}\cdot\pi\cdot r^3,[/tex]• the volume of a cylinder of radius r and heigth h is:
[tex]V_C=h\cdot\pi\cdot r^2.[/tex]If the volume of the sphere (Vs) is 2/3 the volume of the cylinder (Vc), we have:
[tex]\begin{gathered} V_S=\frac{2}{3}\cdot V_C, \\ \frac{4}{3}\cdot\pi\cdot r^3=\frac{2}{3}\cdot h\cdot\pi\cdot r^2. \end{gathered}[/tex]Solving for h, we find that:
[tex]h=2r.[/tex]We have found that the height of the cylinder is two times its radius.
Answer
• We have a sphere and cylinder with the same radius.
,• We know that the volume of the sphere is
[tex]V_S=\frac{2}{3}\cdot V_C.[/tex]• By replacing the formulas of each volume, we find that the heigh of the cylinder is:
[tex]h=2r.[/tex]
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