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 ___________.

Answer 1

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)

$\therefore 2\mathrm{\pi }r\left(r+h\right)=1628{\mathrm{cm}}^2$

$\Rightarrow 2\times \frac{22}{7}\times r\times 37\mathrm{cm}=1628{\mathrm{cm}}^2$ [Using (1)]

$\Rightarrow r=\frac{1628\times 7}{44\times 37}=7\mathrm{cm}$ .....(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

$=\mathrm{\pi }{r}^{2}h$

$=\frac{22}{7}\times {\left(7\mathrm{cm}\right)}^2\times 30\mathrm{cm}$ [From (2) and (3)]

$=4620{\mathrm{cm}}^3$

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___.