Question

Sum of the radius of the base and height of a cylinder is 21 cm and the curved surface area of the cylinder is 616 sq.cm,find the total surface area of the cylinder.

Please help me!

Answer 1

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

`r+h=21`

`h=21-r` ...(i)

Curved surface area of the cylinder is

`CSA=2\pi rh`

Curved surface area of the cylinder = 616 sq.cm

`2\pi rh=616`

`2((22)/(7))r(21-r)=616`

`44r(21-r)=616* 7`

`21r-r^2=(616* 7)/(44)`

`21r-r^2=14* 7`

`0=98-21r+r^2`

`0=98-14r-7r+r^2`

`0=14(7-r)-r(7-r)`

`0=(7-r)(14-r)`

`r=7,14`

Using (i), for r=7, h=14 and for r=14, h=7.

Total surface area of the cylinder is

`A=2\pi r(r+h)`

For r=7 and h=14,

`A=2((22)/(7))(7)(7+14)`

`A=44(21)`

`A=924`

For r=14 and h=7,

`A=2((22)/(7))(14)(14+7)`

`A=88(21)`

`A=1848`

Therefore, the total surface area of the cylinder is either 924 sq.cm or 1848 sq. cm.