question_answer

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder,\[\left( use\,\pi =\frac{22}{7} \right)\]

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), \[h=30\])

\[=4620\text{ }c{{m}^{3}}\]