Question

What is the volume in liters of a rectangular tank which measures \(2.0 \mathrm{~m}\) by \(50 \mathrm{~cm}\) by \(200 \mathrm{~mm} ?\)

Short answer

The volume of the rectangular tank is 200 liters.

Step-by-step solution

Convert all measurements to meters

We need to have all measurements in meters before performing the volume calculation. Therefore, we will convert the width and height to meters: - Width: 50 cm = 0.5 meters (1 meter = 100 cm) - Height: 200 mm = 0.2 meters (1 meter = 1000 mm) Now, we have the dimensions in meters: length = 2.0 m, width = 0.5 m, and height = 0.2 m.

Calculate the volume in cubic meters

To find the volume of the rectangular tank in cubic meters, we simply multiply the length, width, and height: Volume = Length × Width × Height Volume = (2.0 m) × (0.5 m) × (0.2 m) = 0.2 m³ So, the volume of the tank is 0.2 cubic meters.

Convert the volume to liters

Now, we need to convert the volume from cubic meters to liters. We know that 1 cubic meter = 1000 liters: Volume (in liters) = Volume (in cubic meters) × 1000 Volume (in liters) = 0.2 m³ × 1000 = 200 L Therefore, the volume of the rectangular tank is 200 liters.

Key concepts

Unit Conversion

Unit conversion is the process of converting a measure from one unit to another. It's a critical skill when dealing with measurement problems, ensuring that all measurements are in the same units before performing calculations. In our exercise, we have different units: meters, centimeters, and millimeters.

• Meters (m) are a standard unit of length in the metric system.
• Centimeters (cm) are one-hundredth of a meter, so 1 m = 100 cm.
• Millimeters (mm) are one-thousandth of a meter, so 1 m = 1000 mm.

To solve problems that require unit conversion:

• Identify the units you are working with and determine their conversion factors.
• Multiply or divide by the conversion factor to convert each measurement to the desired unit.

By ensuring all dimensions of the rectangular tank are in meters, you're preparing them for volume calculation. This consistency is vital for accurate and precise calculations.

Rectangular Tank

A rectangular tank is a 3-dimensional object shaped like a box. Each tank has three dimensions: length, width, and height. Calculating its volume involves multiplying these dimensions together.Understanding these terms:

• Length: The longest side of the rectangle.
• Width: The shorter side adjacent to the length.
• Height: The vertical distance from the base to the top.

When dealing with these dimensions, always ensure they are in the same unit for calculations.For example, in this exercise, the width and height were converted from centimeters and millimeters to meters:

• Width: 50 cm = 0.5 m
• Height: 200 mm = 0.2 m

These steps ensure that when you calculate the volume using the formula \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]you're using consistent measurements that lead to an accurate determination of the tank's volume.

Cubic Meters to Liters

Converting cubic meters to liters is straightforward in the metric system as it relies on a simple relationship. The metric system is organized in powers of ten, making conversions efficient. In this system,

• 1 cubic meter (m³) equals 1000 liters (L).

Understanding this relationship means that to convert from cubic meters to liters, you just multiply the volume in cubic meters by 1000.In the given exercise, we first find the volume of the tank in cubic meters: \[ \text{Volume} = 0.2 \, \text{m}^3 \]To convert this into liters:\[ \text{Volume in Liters} = 0.2 \, \text{m}^3 \times 1000 = 200 \, L \]This straightforward conversion makes it easy to interpret measurements in familiar terms. Knowing the basic conversion factor helps you move effortlessly between these units without confusion, making practical applications much simpler when dealing with volumes in everyday scenarios.