The capacity of a rectangular tank is 15000 litres. What is the height of the tank if its length is 75 cm and its width is 105 cm?
Answer (2)
Convert the capacity of the tank from litres to cubic centimeters: 15000 litres = 15000000 cm 3 .
Apply the formula for the volume of a rectangular tank: V = length × width × height .
Substitute the given values: 15000000 = 75 × 105 × h .
Solve for the height: h = 75 × 105 15000000 ≈ 1904.76 cm .
The height of the tank is 1904.76 cm .
Explanation
Problem Analysis We are given the capacity of a rectangular tank as 15000 litres, its length as 75 cm, and its width as 105 cm. Our goal is to find the height of the tank.
Convert Litres to Cubic Centimeters First, we need to convert the capacity from litres to cubic centimeters. Since 1 litre is equal to 1000 cubic centimeters, we have: 15000 litres = 15000 litres × 1000 litre cm 3 = 15000000 cm 3
Apply the Volume Formula The volume of a rectangular tank is given by the formula: V = length × width × height We are given the length as 75 cm, the width as 105 cm, and the volume as 15000000 cm 3 . Let the height be h cm. Substituting these values into the formula, we get: 15000000 = 75 × 105 × h
Solve for Height Now, we solve for h :
h = 75 × 105 15000000 h = 7875 15000000 h ≈ 1904.76
Final Answer Therefore, the height of the tank is approximately 1904.76 cm.
Examples
Understanding the volume and dimensions of rectangular tanks is crucial in various real-world applications. For instance, in aquaculture, calculating the volume of fish tanks helps determine the number of fish that can be safely accommodated. Similarly, in agriculture, knowing the dimensions and capacity of water tanks is essential for irrigation planning and water resource management. In construction, calculating the volume of concrete needed for a rectangular foundation ensures accurate material estimation and cost management. These examples highlight how the principles of volume calculation are fundamental in diverse fields, enabling efficient and sustainable practices.
The height of the tank can be calculated to be approximately 1904.76 cm after converting its capacity from litres to cubic centimeters and using the volume formula for a rectangular tank.
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