Question : The circumference of the base of a cylindrical vessel is 158.4 cm and its height is 1 m. How many litres of water can it hold (correct to one decimal place)?
(Take $\left.x-\frac{22}{7}\right)$
Option 1: 186.4
Option 2: 200.8
Option 3: 198.2
Option 4: 199.6
Correct Answer: 199.6
Solution :
Circumference of the circle of radius $r$ = $2\pi r$
⇒ $2\pi r = 158.4\ \text{cm}$
⇒ $r = 25.2\ \text{cm}$
Height of cylinder = 100 cm
Volume of cylinder = $\pi r^2h$
= $\frac{22}{7} × 25.2 × 25.2 × 100$
= $199584\ \text{cm}^3$
The volume of the cylinder in litres = 199584 × 0.001 litre = 199.584 litres
Hence, the correct answer is 199.6 litres.
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