Find the ratio between the total surface area of a cylinder to its curved surface area,

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:

Let $S_{1}$ and $S_{2}$ be the total surface area and curved surface area, respectively.

Given :

Height, $h=7.5 \mathrm{~cm}$

Radius, $r=3.5 \mathrm{~cm}$

$\mathrm{~S}_{1}=2 \pi r(r+h)$

$\mathrm{S}_{2}=2 \pi r h$

According to the question:

$\frac{S_{1}}{S_{2}}=\frac{2 \pi r(r+h)}{2 \pi r h}$

$\frac{S_{1}}{S_{2}}=\frac{\mathrm{r}+\mathrm{h}}{\mathrm{h}}$

$\frac{S_{1}}{S_{2}}=\frac{3.5+7.5}{7.5}$

$\frac{S_{1}}{S_{2}}=\frac{11}{7.5}=\frac{110}{75}=\frac{22}{15}$

Therefore, the ratio is $22: 15$.

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