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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.
Solution
\[\text{ Let S_1 and S_2 be the total surface area and curved surface area, respectively } . \]
\[\text{ Given: } \]
\[\text{ Height, h = 7 . 5 cm } \]
\[\text{ Radius, r = 3 . 5 cm } \]
\[ S_1 = 2\pi r\left( r + h \right)\]
\[ S_2 = 2\pi rh\]
\[\text{ According to the question: } \]
\[\frac{S_1}{S_2} = \frac{2\pi r\left( r + h \right)}{2\pi rh}\]
\[\frac{S_1}{S_2} = \frac{r + h}{h}\]
\[\frac{S_1}{S_2} = \frac{3 . 5 + 7 . 5}{7 . 5}\]
\[\frac{S_1}{S_2} = \frac{11}{7 . 5} = \frac{110}{75} = \frac{22}{15}\]
\[\text{ Therefore, the ratio is } 22: 15 .\]
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