Question : The total surface area of a right circular cylinder is 1848 cm². The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $\pi=\frac{22}{7}$)
Option 1: 4312 cm³
Option 2: 3696 cm³
Option 3: 4002 cm³
Option 4: 4851 cm³

Question

Question : The total surface area of a right circular cylinder is 1848 cm². The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $\pi=\frac{22}{7}$)

Option 1: 4312 cm³

Option 2: 3696 cm³

Option 3: 4002 cm³

Option 4: 4851 cm³

Team Careers360 · Accepted Answer

Correct Answer: 4312 cm³

Solution : Let the radius of the base of the cylinder as $r$ and the height of the cylinder as $h$.
The total surface area (TSA) of a right circular cylinder is,
$⇒ ext{TSA} = 2\pi r(r + h)$
The curved surface area (CSA) of a right circular cylinder is,
$⇒ ext{CSA} = 2\pi rh$
Given that the ratio of TSA to CSA is 3 : 1.
$⇒\frac{ ext{TSA}}{ ext{CSA}} = \frac{2\pi r(r + h)}{2\pi rh} = \frac{3}{1}$
$⇒\frac{r + h}{h} = \frac{3}{1}$
$⇒r = 2h$
$ ext{TSA} = 2\pi r(r + h) = 1848$
Substituting $\pi = \frac{22}{7}$,
$⇒2 imes\frac{22}{7} imes r(r + \frac{r}{2}) = 1848$
$⇒2 imes\frac{22}{7} imes r( \frac{3r}{2}) = 1848$
$⇒r^2=7 imes7 imes4$
$⇒r=14$
$⇒h=\frac{r}{2}=7$ cm
The volume ($V$) of a right circular cylinder is,
$⇒V = \pi r^2 h$
$⇒V = \frac{22}{7} imes(14)^2 imes 7$
$⇒V = 4312$ cm³
Hence, the correct answer is 4312 cm³.

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Question : The total surface area of a right circular cylinder is 1848 cm2. The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take π=227)Option 1: 4312 cm3 Option 2: 3696 cm3 Option 3: 4002 cm3 Option 4: 4851 cm3

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Question : The total surface area of a right circular cylinder is 1848 cm². The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $π = \frac{22}{7}$ )
Option 1: 4312 cm³
Option 2: 3696 cm³
Option 3: 4002 cm³
Option 4: 4851 cm³