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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.
Solution
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
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