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 = πr2 h
= 22/7 * 72 * 30
= 4620 m³
∴ Volume of the cylinder is 4620 m³