Question

The radius of the base and the height of a solid right circular cylinder are in the ratio 2 : 3 and its volume is 1617 cm³. Find the total surface area of the cylinder.

Answer 1

Let the radius of the cylinder be 2x cm and its height be 3x cm. 

Then,Volume of the cylinder`=pi"r"^2"h"`

`=22/7xx(2x)^2xx3x`

Therefore, 

`22/7xx(2x)^2xx3x=1617`

`=>22/7xx4x^2xx3x=1617`

`=> 22/7xx12x^3 = 1617`

`=>x^3=(1617+7/22xx12)`

`=> x^3=(7/2xx7/2xx7/2)`

`=> x^3 = (7/2)^3`

`=> x = 7/2`

Now, r = 7 cm and `"h" = 21/2  "cm"`

Hence,the total surface area of the cylinder:

(2πrh + 2πr²)

= 2πr(h + r)

`= 2xx22/7xx7xx(21/2+7)"cm"^`

`= (2xx(22)/7xx7xx(35)/2) "cm"^2 `

= 770 cm²