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Question

If the sum of the radius of the base and the height of a solid cylinder is 37 m and the total surface area of the cylinder is 1628 m2, then its volume is ___________.

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Solution


Let r and h be the radius and height of the cylinder, respectively.

Now,

r + h = 37 m (Given) .....(1)

Total surface of the cylinder = 1628 m2 (Given)

2πrr+h=1628 cm2

2×227×r×37 cm=1628 cm2 [Using (1)]

r=1628×744×37=7 cm .....(2)

Substituting the value of r in (1), we get

7 cm + h = 37 cm

⇒ h = 37 − 7 = 30 cm .....(3)

∴ Volume of the solid cylinder

=πr2h

=227×7 cm2×30 cm [From (2) and (3)]

=4620 cm3

Thus, the volume of the solid cylinder is 4620 cm3.

If the sum of the radius of the base and the height of a solid cylinder is 37 m and the total surface area of the cylinder is 1628 m2, then its volume is ___4620 cm3___.

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