Answer :
To find how many litres of water a cylindrical vessel can hold, we need to calculate its volume. We're given the circumference of the base and the height of the cylinder.
Step 1: Find the Radius of the Base
The formula for the circumference [tex]C[/tex] of a circle is:
[tex]C = 2\pi r[/tex]
where [tex]r[/tex] is the radius.
Given the circumference [tex]C = 176 \text{ cm}[/tex] and [tex]\pi = \frac{22}{7}[/tex], we can solve for [tex]r[/tex]:
[tex]176 = 2 \times \frac{22}{7} \times r[/tex]
[tex]r = \frac{176 \times 7}{2 \times 22}[/tex]
[tex]r = \frac{1232}{44}[/tex]
[tex]r = 28 \text{ cm}[/tex]
Step 2: Calculate the Volume of the Cylinder
The formula for the volume [tex]V[/tex] of a cylinder is:
[tex]V = \pi r^2 h[/tex]
where [tex]h[/tex] is the height.
The height given is 21 mm. Converting this to centimeters (since we need consistent units), we have:
[tex]h = 2.1 \text{ cm}[/tex]
Now, substitute the values:
[tex]V = \frac{22}{7} \times (28)^2 \times 2.1[/tex]
[tex]V = \frac{22}{7} \times 784 \times 2.1[/tex]
[tex]V = \frac{22}{7} \times 1646.4[/tex]
[tex]V = 5174.4 \text{ cm}^3[/tex]
Step 3: Convert Volume to Litres
Since 1 litre = 1000 cm³, the volume in litres is:
[tex]V = \frac{5174.4}{1000}[/tex]
[tex]V = 5.1744 \text{ litres}[/tex]
Therefore, the cylinder can hold approximately 5.1744 litres of water. The correct multiple-choice option is 5.1744.
