Question

If the area of the curved surface and the circumference of the base of a right circular cylinder are 4400 cm² and 110 cm respectively, then the volume of the cylinder is _________.

Answer 1

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

Curved surface area of the cylinder = 4400 cm² (Given)

∴ 2$\mathrm{\pi }$rh = 4400 cm² .....(1)

Also, circumference of the base = 110 cm (Given)

∴ 2$\mathrm{\pi }$r = 110 cm .....(2)

$\Rightarrow 2\times \frac{22}{7}\times r=110\mathrm{cm}$

$\Rightarrow r=\frac{110\times 7}{44}=\frac{35}{2}\mathrm{cm}$

Now, dividing (1) by (2), we get

$\frac{2\mathrm{\pi }rh}{2\mathrm{\pi }r}=\frac{4400{\mathrm{cm}}^2}{110\mathrm{cm}}$

$\Rightarrow h=40\mathrm{cm}$

∴ Volume of the cylinder

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

$=\frac{22}{7}\times {\left(\frac{35}{2}\mathrm{cm}\right)}^2\times 40\mathrm{cm}$

$=\frac{22}{7}\times \frac{35}{2}\times \frac{35}{2}\times 40{\mathrm{cm}}^3$

$=38500{\mathrm{cm}}^3$

Thus, the volume of the cylinder is 38500 cm³.

If the area of the curved surface and the circumference of the base of a right circular cylinder are 4400 cm² and 110 cm respectively, then the volume of the cylinder is ___38500 cm³___.