The ratio of the total surface area to the lateral surface area of the

1.	The ratio of the total surface area to the lateral surface area of the cylinder is 5 : 3. Find the height of the cylinder if the radius of the cylinder is 12 cm?
Answer» Let the height and radius of the cylinder be h and r respectively. Then, \(\frac{\text{Total surface area}}{\text{lateral surface area}}\) = \(\frac{2πrh+2πr^2}{2πrh}\) = \(\frac{2πr(r+h)}{2πrh}\) = \(\frac{r+h}{h}\) Given, \(\frac{r+h}{h}\) = \(\frac53\) ⇒ \(\frac{12+h}{h}\) = \(\frac53\) ⇒ 36 + 3h = 5h ⇒ 2h = 36 ⇒ h = 18 cm.

The ratio of the total surface area to the lateral surface area of the cylinder is 5 : 3. Find the height of the cylinder if the radius of the cylinder is 12 cm?

Answer»

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

\(\frac{\text{Total surface area}}{\text{lateral surface area}}\) = \(\frac{2πrh+2πr^2}{2πrh}\) = \(\frac{2πr(r+h)}{2πrh}\) = \(\frac{r+h}{h}\)

Given, \(\frac{r+h}{h}\) = \(\frac53\) ⇒ \(\frac{12+h}{h}\) = \(\frac53\) ⇒ 36 + 3h = 5h ⇒ 2h = 36 ⇒ h = 18 cm.