Question

The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 cm². Find the volume of the cylinder.

Answer 1

Given data is as follows:

 h + r = 37 cm

Total surface area of the cylinder = 1628 cm²

We have to find the volume of the cylinder.

It is given that,

Total surface area = 1628 cm² 

That is,

`2pirh + 2pir^2 = 1628 `

`2pir ( h +r ) = 1628`

But it is already given in the problem that,

h + r = 37 cm

Therefore,

 `2pir xx 37`= 1628

 `2 xx 22/7 xx r xx 37`= 1628

r = 7 cm

Since  h + r = 37 cm 

We have,

 h + 7 = 37 cm

h = 30 cm

Now that we know both height and radius of the cylinder, we can easily find the volume.

Volume = `pir^2h`

Volume = `22/7 xx 7xx7xx30`

Volume = 4320  cm³

Hence, the volume of the given cylinder is 4620 cm³