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
Correct Answer: 4312 cm 3
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,
$⇒\text{TSA} = 2\pi r(r + h)$
The curved surface area (CSA) of a right circular cylinder is,
$⇒\text{CSA} = 2\pi rh$
Given that the ratio of TSA to CSA is 3 : 1.
$⇒\frac{\text{TSA}}{\text{CSA}} = \frac{2\pi r(r + h)}{2\pi rh} = \frac{3}{1}$
$⇒\frac{r + h}{h} = \frac{3}{1}$
$⇒r = 2h$
$\text{TSA} = 2\pi r(r + h) = 1848$
Substituting $\pi = \frac{22}{7}$,
$⇒2\times\frac{22}{7}\times r(r + \frac{r}{2}) = 1848$
$⇒2\times\frac{22}{7}\times r( \frac{3r}{2}) = 1848$
$⇒r^2=7\times7\times4$
$⇒r=14$
$⇒h=\frac{r}{2}=7$ cm
The volume ($V$) of a right circular cylinder is,
$⇒V = \pi r^2 h$
$⇒V = \frac{22}{7} \times(14)^2\times 7$
$⇒V = 4312$ cm
3
Hence, the correct answer is 4312 cm
3
.
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