Respuesta :
Solution:
The ratio of the radius to the height of the cylinder is
[tex]2\colon3[/tex]Let the radius be
[tex]r=2x[/tex]Let the height be
[tex]h=3x[/tex]The volume of the cylinder is given below as
[tex]V=1617cm^3[/tex]Concept:
The volume of a cylinder is given below as
[tex]V_{\text{cylinder}}=\pi\times r^2\times h[/tex]By substituting values, we will have
[tex]\begin{gathered} V_{\text{cylinder}}=\pi\times r^2\times h \\ 1617=\frac{22}{7}\times(2x)^2\times(3x) \\ 1617=\frac{22}{7}\times4x^2\times3x \\ 1617\times7=264x^3 \\ \text{divdie both sides by 264} \\ \frac{264x^3}{264}=\frac{1617\times7}{264} \\ x^3=\frac{343}{8} \\ x=\sqrt[3]{\frac{343}{8}} \\ x=\frac{7}{2} \end{gathered}[/tex]The radius therefore will be
[tex]\begin{gathered} r=2x=2\times\frac{7}{2} \\ r=7cm \end{gathered}[/tex]The height of the cylinder will be
[tex]\begin{gathered} h=3x=3\times\frac{7}{2} \\ h=\frac{21}{2}cm \end{gathered}[/tex]The formula for the total surface area of a cylinder is given below as
[tex]T\mathrm{}S\mathrm{}A=2\pi r(r+h)[/tex]By substituting the values, we will have
[tex]\begin{gathered} TSA=2\pi r(r+h) \\ TSA=2\times\frac{22}{7}\times7(7+\frac{21}{2}) \\ TSA=44(7+\frac{21}{2}) \\ TSA=44\times7+44\times\frac{21}{2} \\ TSA=308+462 \\ TSA=770cm^2 \end{gathered}[/tex]Hence,
The total surface area of the cylinder is = 770cm²
