This question sum of the radius of the base and the height of a solid cylinder is given by using volume and surface area relation find volume. This question from RS Aggarwal book exercise 17A problem number 7 . page number 787.

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# The sum of the radius of the base and the height of a solid cylinder is 37 meters. If the total surface area of the cylinder be 1628 sq. meters, then find its volume.

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Let radius = r and

Height = h

The sum of the radius of the base and the height of a solid cylinder is 37 m.

r + h = 37 m …(given)

Total surface area of the cylinder = 2πr(r + h)

1628 = 2πr(37)

r = 7

From (given): 7 + h = 37

h = 30

Again,

Volume of the cylinder = πr

^{2}h= 22/7 * 7

^{2}* 30= 4620 m³

∴ Volume of the cylinder is 4620 m³