To find the radius and volume of the cylindrical vessel, we will use the given circumference and height along with the formula for the volume of a cylinder.
i. Finding the Radius
The formula for the circumference (C) of a cylinder is given by:
C = 2 × π × r
Where:
- C = Circumference
- r = Radius
- π is approximately 22/7 as per the problem statement
Given that the circumference is 132 cm, we set up the equation:
132 = 2 × (22/7) × r
Simplifying this, we can isolate r:
132 = (44/7) × r
Now, multiplying both sides by 7 to eliminate the fraction:
924 = 44 × r
Dividing both sides by 44 gives us:
r = 924 / 44 = 21 cm
ii. Finding the Volume
Now that we have the radius, we can calculate the volume (V) of the cylinder using the formula:
V = π × r2 × h
Where:
- V = Volume
- h = Height of the cylinder (25 cm)
Substituting the known values:
V = (22/7) × (21)2 × 25
Calculating (21)2 first:
441.
Now, substituting back into the volume equation:
V = (22/7) × 441 × 25
Calculating 441 × 25:
11025.
Now substituting in:
V = (22/7) × 11025
Calculating that gives:
V = 34650 / 7 = 4950 cm3
Therefore, the radius of the cylindrical vessel is 21 cm and the volume is 4950 cm3.