Volume of Rectangular Tank

Volume of a Rectangular Tank is an easy math topic for the students. Volume of a rectangular tank helps us to find out the space a tank can hold with the help of easy steps and simple formula. It can be used by students in real life to better understand water tanks, storage boxes and containers.

What Is the Volume of a Rectangular Tank?

The volume of a rectangular tank is the total amount of space inside the tank. It tells you the maximum quantity of liquid the tank can hold when completely filled.

Volume = l × w × h

Formula for Volume of a Rectangular Tank

Volume = Length × Width × Height

V = l × w × h

Where:

l = length of the tank

w = width of the tank

h = height of the tank

Formula in Cubic Units

If measurements are in metres: Volume = cubic metres (m³)

If measurements are in centimetres: Volume = cubic centimetres (cm³)

If measurements are in feet: Volume = cubic feet (ft³)

1 m × 1 m × 1 m = 1 m³ (one cubic metre)

Formula in Litres

1 cubic metre (m³) = 1000 litres

1 cubic centimetre (cm³) = 0.001 litres

1000 cm³ = 1 litre

Volume in litres = Volume in m³ × 1000

How to Calculate the Volume of a Rectangular Tank

Step 1: Measure Length

Measure the longest horizontal dimension of the tank.

Use a tape measure from inside the tank for accuracy.

      ←———————————————→

      ←    Length (l)  →

Always measure from INSIDE the tank

(exclude wall thickness for water capacity).

Step 2: Measure Width

Measure the shorter horizontal dimension of the tank.

This is perpendicular to the length.

Step 3: Measure Height

Measure the vertical depth of the tank from bottom to top.

For open tanks, measure the water level

height for ACTUAL volume of water.

Step 4: Apply the Formula

V = l × w × h

Volume of Rectangular Tank Formula Explained

Length × Width × Height

Step 1: l × w = Base Area

        This gives you the bottom surface of the tank.

Step 2: Base Area × h = Volume

        Stack the base area upward to height h.

Volume fills the entire 3D space.

Understanding Cubic Units

CUBIC UNIT COMPARISON:

1 cm³ = size of a sugar cube (tiny)

1 litre = 1000 cm³ = a water bottle

1 m³ = 1000 litres = a large water tank

How to Convert Cubic Metres to Litres

Cubic Metres to Litres

CONVERSION FORMULA:

Litres = Cubic metres × 1000

Examples:

1 m³ = 1000 L

2 m³ = 2000 L

0.5 m³ = 500 L

3.6 m³ = 3600 L

CONVERSION TABLE:

Cubic Metres (m³)	Litres (L)
0.5 m³	500 L
1.0 m³	1,000 L
1.5 m³	1,500 L
2.0 m³	2,000 L
5.0 m³	5,000 L
10.0 m³	10,000 L

Cubic Centimetres to Litres

CONVERSION FORMULA:

Litres = Cubic centimetres ÷ 1000

Examples:

1000 cm³ = 1 litre

5000 cm³ = 5 litres

500 cm³ = 0.5 litres

12000 cm³ = 12 litres

Cubic Feet to Litres

CONVERSION FORMULA:

Litres = Cubic feet × 28.317

Examples:

1 ft³ = 28.317 litres

2 ft³ = 56.634 litres

10 ft³ = 283.17 litres

Solved Examples on Volume of Rectangular Tank

Example 1: Volume in Cubic Metres

Question: A rectangular water tank is 4 m long, 3 m wide, and 2 m high. Find its volume.

Given:

l = 4 m

w = 3 m

h = 2 m

Formula: V = l × w × h

V = 4 × 3 × 2

V = 24 m³

Answer: Volume = 24 m³

Example 2: Water Capacity in Litres

Question: A rectangular tank measures 2.5 m long, 2 m wide, and 1.5 m high. Find its capacity in litres.

Given:

l = 2.5 m

w = 2.0 m

h = 1.5 m

Step 1: Find volume in m³

V = l × w × h

V = 2.5 × 2 × 1.5

V = 7.5 m³

Step 2: Convert to litres

Litres = 7.5 × 1000

Litres = 7500 litres

Answer: Tank capacity = 7500 litres

Example 3: Tank Filled Halfway

Question: A rectangular tank is 5 m long, 4 m wide, and 3 m high. The tank is filled only halfway. Find the volume of water in it.

Given:

l = 5 m, w = 4 m, full h = 3 m

Water fills only half → water height = 3/2 = 1.5 m

V = l × w × water height

V = 5 × 4 × 1.5

V = 30 m³

In litres = 30 × 1000 = 30,000 litres

Answer: Volume of water = 30,000 litres

Example 4: Capacity of an Underground Tank

Question: An underground rectangular water tank is 6 m long, 3 m wide, and 2.5 m deep. Find: a) Volume in cubic metres b) Capacity in litres c) If a family uses 200 litres per day, how many days will the tank last?

Given:

l = 6 m, w = 3 m, h = 2.5 m

a) Volume = l × w × h

         = 6 × 3 × 2.5

         = 45 m³

b) Capacity in litres:

   = 45 × 1000 = 45,000 litres

c) Days the tank lasts:

   = 45,000 ÷ 200 = 225 days

Answer:

a) 45 m³

b) 45,000 litres

c) 225 days

Volume of Water in a Rectangular Tank

Completely Filled Tank

Volume of water = l × w × h (full height)

       

Volume = l × w × h

Partially Filled Tank

When partially filled:

Volume of water = l × w × d

Where d = depth of water (not full height)

 

Volume of water = l × w × d

Empty space = l × w × (h − d)

Empty Space Calculation

Empty volume = Total volume − Water volume

             = l × w × h − l × w × d

             = l × w × (h − d)

Example:

Tank: l = 3m, w = 2m, h = 2m

Water depth: d = 1.5m

Total volume = 3 × 2 × 2 = 12 m³

Water volume = 3 × 2 × 1.5 = 9 m³

Empty space = 12 − 9 = 3 m³ = 3000 litres

Real Life Applications

Household Water Tanks

A typical home rectangular tank: l = 2 m, w = 1.5 m, h = 1.5 m

V = 2 × 1.5 × 1.5 = 4.5 m³ = 4500 litres

Average family uses 500 − 600 litres per day.

This tank lasts about 7 − 9 days.

Swimming Pools

A small rectangular swimming pool: l = 10 m, w = 5 m, h = 1.5 m

V = 10 × 5 × 1.5 = 75 m³ = 75,000 litres

At ₹5 per 1000 litres:

Cost to fill = 75 × 5 = ₹375

Agricultural Water Storage

A farm water storage tank: l = 10 m, w = 8 m, h = 3 m

V = 10 × 8 × 3 = 240 m³ = 240,000 litres

If crops need 5000 litres per day:

Days covered = 240,000 ÷ 5000 = 48 days

Industrial Tanks

Industrial tanks are often much larger: l = 20 m, w = 15 m, h = 5 m

V = 20 × 15 × 5 = 1500 m³ = 1,500,000 litres

Industrial tanks may store fuel, chemicals,

or process water in factories.

Practice Questions on Volume of Rectangular Tank

Q1: A rectangular tank is 3 m long, 2 m wide, and 1 m high. Find its volume.

V = 3 × 2 × 1 = 6 m³

Answer: 6 m³

Q2: Find the capacity in litres of a tank with dimensions 4 m × 2.5 m × 1.5 m.

V = 4 × 2.5 × 1.5 = 15 m³

Litres = 15 × 1000 = 15,000 litres

Answer: 15,000 litres

Q3: A tank holds 1000 litres when full. What is its volume in m³?

1000 litres ÷ 1000 = 1 m³

Answer: 1 m³

Q4: Find the volume in cm³: l = 50cm, w = 40cm, h = 30cm.

V = 50 × 40 × 30 = 60,000 cm³

Answer: 60,000 cm³

Q5: A rectangular tank is half full. Total capacity = 8000 litres. How much water is in it?

Water = 8000 ÷ 2 = 4000 litres

Answer: 4000 litres

Q6: A rectangular water tank is 5 m long, 4 m wide, and 3 m high. Water is filled to 2 m height. Find: a) Volume of water b) Empty volume remaining

a) Volume of water:

V = 5 × 4 × 2 = 40 m³ = 40,000 litres

b) Empty volume:

Total = 5 × 4 × 3 = 60 m³ = 60,000 litres

Empty = 60,000 − 40,000 = 20,000 litres

Answers:

a) 40,000 litres

b) 20,000 litres

Q7: A family needs 400 litres of water per day. They have a rectangular tank measuring 2 m × 2 m × 2.5 m. For how many days will a full tank last?

V = 2 × 2 × 2.5 = 10 m³ = 10,000 litres

Days = 10,000 ÷ 400 = 25 days

Answer: 25 days

Q8: A rectangular tank costs ₹500 per cubic metre to build. The tank is 6 m long, 4 m wide, and 2 m high. Find the construction cost.

V = 6 × 4 × 2 = 48 m³

Cost = 48 × 500 = ₹24,000

Answer: ₹24,000

Q9: Two rectangular tanks are connected. Tank A: 3m × 2m × 2m. Tank B: 4m × 3m × 1.5m. Find total water storage capacity in litres.

Tank A: V = 3 × 2 × 2 = 12 m³

Tank B: V = 4 × 3 × 1.5 = 18 m³

Total = 12 + 18 = 30 m³ = 30,000 litres

Answer: 30,000 litres

Q10: A rectangular tank is 8 m long and 5 m wide. When water fills it to 3/4 of its height, the volume of water is 90 m³. Find the full height of the tank.

Let full height = h

Water height = 3h/4

V of water = l × w × (3h/4)

90 = 8 × 5 × (3h/4)

90 = 40 × (3h/4)

90 = 30h

h = 3 m

Answer: Full height = 3 m

Verify: 8 × 5 × (3×3/4) = 40 × 2.25 = 90

Q11: A rectangular underground tank is 10 m × 8 m × 4 m. It is currently 60% full. A pump empties it at 500 litres per minute. How long will it take to empty the tank completely?

Total volume = 10 × 8 × 4 = 320 m³ = 320,000 litres

Water in tank = 60% of 320,000 = 192,000 litres

Rate = 500 litres per minute

Time = 192,000 ÷ 500 = 384 minutes

     = 384 ÷ 60 = 6 hours 24 minutes

Answer: 6 hours and 24 minutes

Q12: Three identical rectangular tanks each have dimensions 4 m × 3 m × 2 m. They supply water to a factory that uses 3000 litres per hour. If all three tanks are full at 6 AM, at what time will they run dry?

Volume of one tank = 4 × 3 × 2 = 24 m³ = 24,000 litres

Total volume = 3 × 24,000 = 72,000 litres

Usage rate = 3000 litres per hour

Time to empty = 72,000 ÷ 3000 = 24 hours

Starting at 6 AM:

6 AM + 24 hours = 6 AM next day

Answer: The tanks run dry at 6 AM the next day