Question

Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm.

 

Answer 1

\[\text{ Let S_1 and S_2 be the total surface area and curved surface area, respectively }  . \]

\[\text{ Given: } \]

\[\text{ Height, h = 7 . 5 cm } \]

\[\text{ Radius, r = 3 . 5 cm } \]

\[ S_1 = 2\pi r\left( r + h \right)\]

\[ S_2 = 2\pi rh\]

\[\text{ According to the question: }  \]

\[\frac{S_1}{S_2} = \frac{2\pi r\left( r + h \right)}{2\pi rh}\]

\[\frac{S_1}{S_2} = \frac{r + h}{h}\]

\[\frac{S_1}{S_2} = \frac{3 . 5 + 7 . 5}{7 . 5}\]

\[\frac{S_1}{S_2} = \frac{11}{7 . 5} = \frac{110}{75} = \frac{22}{15}\]

\[\text{ Therefore, the ratio is } 22: 15 .\]