Question

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm².

Answer 1

Data given is as follows:

`"Curved Surface Area"/("Total Surface Area")=(1/2)`

`"Total Surface Area = 616 cm"^2`

We have to find the volume of the cylinder.

From the given data we have,

`"Curved Surface Area"/"Total Surface Area" = (1/2)`

`"Curved Surface Area "= (1/2) xx "Total Surface Area "`

                                    ` =(1/2) xx 616  cm^2`

                                    ` = 308  cm^2`

Also,

`"Curved Surface Area"/"Total Surface Area " = (1/2)`

`(2pirh)/(2pirh + 2 pi r^2) = 1/2`

             `h/(h+r)=1/2`

                    2h = h + r

                     h = r 

We have found out the Curved Surface Area of the cylinder which is 308 cm². 

Curved Surface Area = 308 cm²

`2pirh` =308

Now, let us replace h with r in the above equation since in the previous step we have found that  h = r .

`2pir^2` =308

`2 xx 22/7 xx r^2 = 308`

`r = 7`

Since h = r , h is also equal to 7

Volume = `pi r^2 h`

`=22/7 xx 7 xx 7 xx 7`

Volume = 1078 cm³