Respuesta :
Given:
Sum of the radius of the base and height of a cylinder = 21 cm
Curved surface area of the cylinder = 616 sq.cm
To find:
The total surface area of the cylinder.
Solution:
Let r be the radius of the base and h be the height of the cylinder.
Sum of the radius of the base and height of a cylinder = 21 cm
[tex]r+h=21[/tex]
[tex]h=21-r[/tex] ...(i)
Curved surface area of the cylinder is
[tex]CSA=2\pi rh[/tex]
Curved surface area of the cylinder = 616 sq.cm
[tex]2\pi rh=616[/tex]
[tex]2(\dfrac{22}{7})r(21-r)=616[/tex]
[tex]44r(21-r)=616\times 7[/tex]
[tex]21r-r^2=\dfrac{616\times 7}{44}[/tex]
[tex]21r-r^2=14\times 7[/tex]
[tex]0=98-21r+r^2[/tex]
[tex]0=98-14r-7r+r^2[/tex]
[tex]0=14(7-r)-r(7-r)[/tex]
[tex]0=(7-r)(14-r)[/tex]
[tex]r=7,14[/tex]
Using (i), for r=7, h=14 and for r=14, h=7.
Total surface area of the cylinder is
[tex]A=2\pi r(r+h)[/tex]
For r=7 and h=14,
[tex]A=2(\dfrac{22}{7})(7)(7+14)[/tex]
[tex]A=44(21)[/tex]
[tex]A=924[/tex]
For r=14 and h=7,
[tex]A=2(\dfrac{22}{7})(14)(14+7)[/tex]
[tex]A=88(21)[/tex]
[tex]A=1848[/tex]
Therefore, the total surface area of the cylinder is either 924 sq.cm or 1848 sq. cm.
