Question : The circumference of the base of a cylindrical vessel is 264 cm and its height is 50 cm. The capacity (in litres) of the vessel is:
(Take $\pi=\frac{22}{7}$)
Option 1: 277.2
Option 2: 278.4
Option 3: 280.6
Option 4: 267.4
Correct Answer: 277.2
Solution :
The capacity of a cylindrical vessel is the volume of a cylinder, which is $\pi r^2 h$, where $r$ is the radius of the base and $h$ is the height of the cylinder.
Given that the circumference of the base of the cylinder is 264 cm.
$⇒2\pi r=264$
$⇒r = \frac{264}{2\pi}$ = 42 cm
Substituting, $r = 42$ cm and $h = 50$ cm into the formula,
$⇒V = \pi r^2 h = \frac{22}{7} \times 42^2 \times 50 = 277200 \text{ cm}^3$
Since 1 litre is equal to 1000 cm
3
.
The capacity of the vessel = $\frac{277200}{1000}$ = 277.2 litres
Hence, the correct answer is 277.2.
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