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Question

The sum of height and radius of the base of a solid cylinder is 37 cm. Total surface area f the cylinder is 1628 cm2, Find its volume of the cylinder.

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Solution

Let 'h' be height & 'r' be radius of the base of cylinder.
Also, given that r+h=37cm ------(1)
and TSA of cylinder = 1628cm2 ----(2)
we know TSA of the cylinder = 2πr(h+r)
So,
1628=2πr(37)
r=16282π×37
r=81437π
r=7cm
From equation (1), r+h=37
7+h=37
h=30cm
Now, Volume of the cylinder =πr2h
=3.14×49×30
=46150.8cm2

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