Find the volume of a water tank which is 250cm long, 160cm wide and 80cm deep. A. 20 litres B. 32 litres C. 40 litres D. 320 litres E. 3200 litres
The correct answer and explanation is:
To find the volume of a water tank, we use the formula for the volume of a rectangular prism: Volume=length×width×height\text{Volume} = \text{length} \times \text{width} \times \text{height}
Given:
- Length = 250 cm
- Width = 160 cm
- Depth (Height) = 80 cm
Step 1: Calculate Volume in Cubic Centimeters
Volume=250×160×80=3,200,000 cm3\text{Volume} = 250 \times 160 \times 80 = 3,200,000 \text{ cm}^3
Step 2: Convert Cubic Centimeters to Litres
1 litre = 1000 cm³ Volume in litres=3,200,0001000=3200 litres\text{Volume in litres} = \frac{3,200,000}{1000} = 3200 \text{ litres}
✅ Correct Answer: E. 3200 litres
🔍 Explanation (300 words)
The volume of a solid object like a water tank is the amount of space it occupies. For rectangular tanks, this space is calculated by multiplying its three dimensions: length, width, and height (or depth). In this case, we multiply the tank’s dimensions, all in centimeters: 250 cm×160 cm×80 cm=3,200,000 cm3250 \, \text{cm} \times 160 \, \text{cm} \times 80 \, \text{cm} = 3,200,000 \, \text{cm}^3
However, the options provided are in litres, not in cubic centimeters. To convert between these two units, we use the fact that: 1 litre=1000 cm31 \text{ litre} = 1000 \text{ cm}^3
So we divide 3,200,000 cm³ by 1000 to get: 3,200,0001000=3200 litres\frac{3,200,000}{1000} = 3200 \text{ litres}
This tells us that the tank can hold 3200 litres of water when full.
Understanding unit conversion is essential when dealing with real-world problems like measuring water in tanks. While centimeters are useful for measuring small distances, litres are more appropriate for liquids. By using simple multiplication and unit conversion, you can easily switch between volume in cubic centimeters and litres.
Thus, the volume of the tank is 3200 litres, making option E the correct choice.