A cylindrical vessel with a base circumference of 132 cm and a height of 25 cm can hold 34.65 litres of water.
Understanding the capacity of containers is crucial for various applications, from household tasks to industrial measurements. This guide details how to determine the volume of a cylindrical vessel and convert it into practical units like litres.
How to Calculate the Volume of a Cylinder
To find the volume of a cylindrical vessel, you need two key measurements: the radius of its base and its height. The formula for the volume ($V$) of a cylinder is:
$V = \pi r^2 h$
Where:
- $\pi$ (pi) is a mathematical constant approximately equal to 3.14159 or 22/7.
- $r$ is the radius of the base.
- $h$ is the height of the cylinder.
In this specific case, we are given the circumference ($C$) of the base and the height ($h$).
Step-by-Step Calculation
-
Determine the Radius (r) from the Circumference:
The circumference of a circle is given by the formula $C = 2\pi r$.
Given $C = 132 \text{ cm}$.
$132 \text{ cm} = 2 \times \frac{22}{7} \times r$
$132 \text{ cm} = \frac{44}{7} \times r$
$r = \frac{132 \text{ cm} \times 7}{44}$
$r = 3 \text{ cm} \times 7$
$r = 21 \text{ cm}$ -
Calculate the Volume (V) in Cubic Centimeters:
Now, using the radius ($r = 21 \text{ cm}$) and the given height ($h = 25 \text{ cm}$):
$V = \pi r^2 h$
$V = \frac{22}{7} \times (21 \text{ cm})^2 \times 25 \text{ cm}$
$V = \frac{22}{7} \times 441 \text{ cm}^2 \times 25 \text{ cm}$
$V = 22 \times 63 \text{ cm}^2 \times 25 \text{ cm}$
$V = 1386 \text{ cm}^2 \times 25 \text{ cm}$
$V = 34650 \text{ cm}^3$ -
Convert Volume from Cubic Centimeters to Litres:
Since $1 \text{ litre} = 1000 \text{ cubic centimeters}$ ($1 \text{ L} = 1000 \text{ cm}^3$), we can convert the volume:
$V{\text{litres}} = \frac{34650 \text{ cm}^3}{1000 \text{ cm}^3/\text{L}}$
**$V{\text{litres}} = 34.65 \text{ L}$**
Summary of Vessel Dimensions and Capacity
This table summarizes the key dimensions and the calculated capacity of the cylindrical vessel.
| Measurement Category | Value | Unit |
|---|---|---|
| Circumference of Base | 132 | cm |
| Height | 25 | cm |
| Calculated Radius | 21 | cm |
| Calculated Volume | 34650 | cm³ |
| Capacity | 34.65 | Litres |
This detailed calculation confirms that the cylindrical vessel can indeed hold 34.65 litres of water. Understanding these steps allows for accurate measurement and planning for various uses of cylindrical containers. For more information on units of volume and conversions, you can refer to resources like the National Institute of Standards and Technology (NIST).
