Given:
- Length of the original tank (L) = 5 m
- Width of the original tank (B) = 4 m
- Volume of the original tank (V) = 60 m³
- Volume of the model tank = 480 cm³
Step 1: Find the height of the original tank:
We know that the volume of a rectangular tank is given by:
Volume = Length × Width × Height
So, for the original tank:
60 m³ = 5 m × 4 m × Height
Height = 60 m³ / (5 m × 4 m) = 3 m
Step 2: Set up the proportionality:
Let’s assume the new scale factor is ‘x’:
- Length of the model tank = 5x cm
- Width of the model tank = 4x cm
- Height of the model tank = 3x cm
Step 3: Calculate the scale factor:
We know the volume of the model tank is 480 cm³. So, we can set up the equation:
(5x cm) × (4x cm) × (3x cm) = 480 cm³
Simplifying:
60x³ = 480
Solving for x:
x³ = 8
x = 2
Step 4: Find the length of the model tank:
The length of the model tank is 5x cm. Substituting x = 2, we get:
Length of the model tank = 5 × 2 cm = 10 cm