The ratio between the radius of the base and the height jof a cylinder

1.	The ratio between the radius of the base and the height jof a cylinder is 2 : 3. Find the total surface area of the cylinder, if its volume is 1617 cm3.
Answer» Given, Ratio between radius and height of a cylinder = 2:3 = \(\frac{r}{h}\) = \(\frac{2}{3}\) = 3r = 2h or h \(\frac{3}{2}\)r Volume of cylinder = 1617 cm³ = πr²h = 1617 = \(\frac{22}{7}\)x r² x \(\frac{3}{2}\)r = 1617 = r³ = \(\frac{1617\times 14}{66}\) = 343 = r = \(\sqrt{343}\) = 7 cm Radius = 7 cm Height = \(\frac{3}{2}\) x 7 = \(\frac{21}{2}\) cm = 10.5 cm ∴ total surface area of cylinder = 2πr(h + +r) = 2 x \(\frac{22}{7}\) x 7(7 + 10.5) = 44 x 17.5 = 770 cm²

The ratio between the radius of the base and the height jof a cylinder is 2 : 3. Find the total surface area of the cylinder, if its volume is 1617 cm3.

Answer»

Given,

Ratio between radius and height of a cylinder = 2:3

= \(\frac{r}{h}\) = \(\frac{2}{3}\)

= 3r = 2h or h \(\frac{3}{2}\)r

Volume of cylinder = 1617 cm³

= πr²h = 1617

= \(\frac{22}{7}\)x r² x \(\frac{3}{2}\)r = 1617

= r³ = \(\frac{1617\times 14}{66}\) = 343

= r = \(\sqrt{343}\) = 7 cm

Radius = 7 cm

Height = \(\frac{3}{2}\) x 7 = \(\frac{21}{2}\) cm = 10.5 cm

∴ total surface area of cylinder = 2πr(h + +r) = 2 x \(\frac{22}{7}\) x 7(7 + 10.5) = 44 x 17.5 = 770 cm²