# 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. - Mathematics

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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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 22 Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)
Exercise 22.1 | Q 18 | Page 11