Answer:
Let the radius of base and height of a solid cylinder be r and h respectively. Now, we have, \[r+h=37\text{ }cm\] ...(i) and, T.S.A. of solid cylinder \[=2\pi \text{ }r(r+h)=1628\text{ }c{{m}^{2}}\] \[\Rightarrow 2\pi r(37)=1628\] \[\Rightarrow r=\frac{1628}{37\times 2\times \frac{22}{7}}\] \[r=7\,cm\] \[\therefore \] Volume of the cylinder \[=\pi {{r}^{2}}h\] \[=\frac{22}{7}\times 7\times 7\times 30\] (Using eq. (i), \[h=30\]) \[=4620\text{ }c{{m}^{3}}\]
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