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The circumference of the base of the cylindrical vessel is 154 cm and its height is 49 mm. How many litres of water can it hold? (correct to three pla
Question

The circumference of the base of the cylindrical vessel is 154 cm and its height is 49 mm. How many litres of water can it hold? (correct to three places of decimals, use π = 22/7)

A.

9.244

B.

2.439

C.

3.924

D.

4.329

Correct option is A

Given:
Circumference of the base of the cylinder = 154 cm
Height of the cylinder = 49 mm = 4.9 cm (since 1 cm = 10 mm)
π=227\pi = \frac{22}{7}​​
Formula Used:
The formula for the volume of a cylinder is:
V=πr2hV = \pi r^2 h​​
Where:
r is the radius of the base of the cylinder,
h is the height of the cylinder.
Circumference of a circle = 2πr
Solution:

154=2×227×r154 = 2 \times \frac{22}{7} \times r ​​

154=447×r154 = \frac{44}{7} \times r​​

r=154×744=107844=24.5 cmr = \frac{154 \times 7}{44} = \frac{1078}{44} = 24.5 \text{ cm}​​

Now, using the formula for the volume of a cylinder:

V=227×(24.5)2×4.9V = \frac{22}{7} \times (24.5)^2 \times 4.9​​

V=227×600.25×4.9V = \frac{22}{7} \times 600.25 \times 4.9​​

V=227×2941.225=9243.85 cubic cmV = \frac{22}{7} \times 2941.225 = 9243.85 \text{ cubic cm}​​

Now, Since 1 liter = 1000 cubic cm,
the Volume in liters is:
V=9243.8510009.244 litersV = \frac{9243.85}{1000} \approx \bf9.244 \text{ liters}​​

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