Question

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If its volume is 1617 cm³, the total surface area of the cylinder is ______.

Options

• 308 cm²

• 462 cm²

• 540 cm²

• 770 cm²

Answer 1

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If its volume is 1617 cm³, the total surface area of the cylinder is 770 cm².

Let the common multiple be x.

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 = (1617xx7/22xx1/12)`

`=>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

`=(2pi"rh"+2pi"r"^2)`

`= 2pi"r"(2xx22/7xx7xx35/2)"cm"^2`

= 770 cm²