Volume of Rectangular Tank

The volume of a rectangular tank is the capacity of the rectangular tank, which signifies the amount of any liquid or conditionally any material it can hold or the amount of liquid that can be immersed in it. The shape of a rectangular tank is that of a rectangle or cuboidal. Thus, the formula for volume or capacity of a rectangular tank can be calculated in a similar way to that of the volume of a cuboid or a rectangular box. The volume of a rectangular tank is represented in cubic units.

The volume of a rectangular tank is defined as the amount of liquid that can be held by the rectangular tank. The rectangular tank has a length, breadth, and height which a cuboid in shape. This tank is a three-dimensional shaped object whose volume is given in cubic units, that is m³, cm³, in³ or ft³, etc. As the rectangular tank is three-dimensional thus, the volume of the rectangular tank also lies in a three-dimensional plane.

The volume of a rectangular tank, i.e, the capacity of the rectangular tank, can be calculated by finding the volume of the cuboidal structured tank. Let the area of a rectangular base be "A", the height of the tank be "h" and the volume of the rectangular tank be "V". Then, the volume of the rectangular tank is given by multiplying the base area and height.

The volume of the rectangular tank, V = Base Area × Height
The volume of the rectangular tank, V = l × b × h

The filled volume of a rectangular tank is a shorter height with a similar length and width. Thus, the new height is the fill height or f. Therefore, the filled volume of a rectangular tank is given as, V(fill) = l × b × f where, l is the length of the rectangular tank, b is the breadth of the rectangular tank, h is the height of the rectangular tank and f is the height of the level of water filled in the tank.

Before starting with the volume of the rectangular tank, let us first understand the concept of volume. The structure of a rectangular tank is very similar to that of a cuboid. Let us compare this structure with a stack of sheets. The stacked sheets form a cuboid. The dimensions of this cuboid can be given as:

l = Length of the base = Length of the rectangular sheet
b = Breadth of the base = Breadth of the rectangular sheet
h = Height of the tank = Height of the stacked sheets

The volume of a rectangular tank can thus be calculated as,

The volume of rectangular tank = Volume of cuboid formed by stacked sheets

V = Base Area × Height
⇒ V = l × b × h

The filled volume of a rectangular tank is given as V(fill) = l × b × f

Thus, we follow the steps shown below to find the volume of the rectangular tank.

• Step 1: Identify the length, breadth, and height of the rectangular tank.
• Step 2: Find the volume using the formula = l × b × h.
• Step 3: The filled volume of the tank can be calculated using the formula = l × w × f
• Step 4: Represent the final answer in cubic units.

Example: What is the volume of the rectangular tank and filled volume of the rectangular tank if the dimensions of the rectangular tank are 20 units × 10 units × 6 units and it is filled to a height of 4 units.
Solution: Given the dimensions of the rectangular tank are, 20 units × 10 units × 6 units and f = 4 units

As we know, the volume of rectangular tank is V = l × b × h
⇒ V = 20 × 10 × 6 = 1200 unit³

The filled volume of the tank is V(fill) = l × w × f
⇒ V(fill) = 20 × 10 × 4 = 800 unit³

Therefore, the volume of the rectangular tank is 1200 unit³ and the filled volume of the rectangular tank is 800 unit³.

What is the Volume of the Rectangular Tank?

The volume of a rectangular tank is the capacity of the rectangular tank, which signifies the amount of any liquid or conditionally any material it can hold or the amount of liquid that can be immersed in it. The shape of a rectangular tank is that of a rectangle or cuboidal.

What is the Filled Volume of a Rectangular Tank?

The filled volume of a rectangular tank is defined as the space occupied by any liquid in the tank. The filled volume of a rectangular tank will always be less than or equal to the volume of the rectangular tank as it depends on the height till which the rectangular tank is filled.

What is the Formula of Volume of the Rectangular Tank?

The formula of volume of the rectangular tank is given as, V = l × b × h where "l" is the length of the base, "b" is the breadth of the base, "h" is the height of the tank and "V" is the volume of the rectangular tank. The volume of the rectangular tank depends on these three dimensions directly.

What is the Formula of Filled Volume of the Rectangular Tank?

The formula of filled volume of the rectangular tank is given as, V(fill) = l × b × f where "l" is the length of the rectangular tank, "b" is the breadth of the rectangular tank, "f" is the height of the level of water filled in the tank and "V(fill)" is the filled volume of the rectangular tank.

How to Calculate the Volume of the Rectangular Tank?

We can calculate the volume of the rectangular tank using the following steps:

• Step 1: Identify the given dimensions as length, breadth, and height of the rectangular tank.
• Step 2: Now, use the volume of the rectangular tank formula, V = l × b × h to determine its value.
• Step 3: Represent the obtained answer in cubic units.

How to Find the Volume of Rectangular Tank If the Units of Dimensions of a Rectangular Tank Are Different?

If the units of dimensions of a rectangular tank are different we calculate the volume of the rectangular tank using the following steps:

• Step 1: Identify which of the given dimensions are the length, breadth, and height of the rectangular tank.
• Step 2: Now change the units of dimensions of any two dimensions in the unit of the third dimension.
• Step 3: Multiply all the three dimensions of the rectangular tank using the formula, V = l × b × h to determine its value.
• Step 4: Represent the obtained answer in Step 3 in cubic units.

Do the Order of Height, Width, and Length Matter While Calculating the Volume of a Rectangular Tank?

No, the order of height, width, and length does not matter because we need to multiply all three quantities to determine the volume of a rectangular tank. As multiplication is commutative, thus, the product of the three quantities will always result in the same value irrespective of their order.