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
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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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