Let's work through the questions from the image step by step.

Part (a)

A rectangular prism has length $l$ cm, width $w$ cm, and height $h$ cm. We need to write an expression for the capacity of the container measured in different units.

1. i) in cm³ (cubic centimeters):

   • The volume $V$ of the rectangular prism is given by: $V = l \times w \times h \, \text{cm}^3$ Since the dimensions are in centimeters, the volume is already expressed in cubic centimeters.

2. ii) in mL (milliliters):

   • 1 cm³ = 1 mL (since 1 mL is defined as 1 cm³ in volume). Therefore, the volume in milliliters is: $V = l \times w \times h \, \text{mL}$

3. iii) in L (liters):

   • 1 liter (L) = 1000 cm³. To convert from cubic centimeters to liters, we divide by 1000: $V = \frac{l \times w \times h}{1000} \, \text{L}$

4. iv) in kL (kiloliters):

   • 1 kiloliter (kL) = 1,000,000 cm³ (since 1 kL = 1000 L and 1 L = 1000 cm³). To convert from cubic centimeters to kiloliters, we divide by 1,000,000: $V = \frac{l \times w \times h}{1,000,000} \, \text{kL}$

Part (b)

A rectangular prism has length $l$ m, width $w$ m, and height $h$ m. We need to write an expression for the capacity of the container in different units.

1. i) in m³ (cubic meters):

   • The volume of the rectangular prism is given by: $V = l \times w \times h \, \text{m}^3$ Since the dimensions are in meters, the volume is already expressed in cubic meters.

2. ii) in L (liters):

   • 1 m³ = 1000 liters. To convert from cubic meters to liters, we multiply by 1000: $V = l \times w \times h \times 1000 \, \text{L}$

3. iii) in kL (kiloliters):

   • 1 m³ = 1 kiloliter (kL), so the volume in kiloliters is: $V = l \times w \times h \, \text{kL}$

4. iv) in ML (megaliters):

   • 1 megaliter (ML) = 1000 m³. To convert from cubic meters to megaliters, we divide by 1000: $V = \frac{l \times w \times h}{1000} \, \text{ML}$

Would you like more details on any part of the solution?

Related Questions:

1. How do you convert between cubic meters and liters in other shapes (e.g., spheres)?
2. What is the general formula for the volume of a rectangular prism?
3. How would the formula change if the prism had a slanted face (i.e., became a parallelepiped)?
4. What is the relationship between milliliters and cubic centimeters?
5. How do you calculate volume when given different units for each dimension?

Tip:

Always ensure that the units for length, width, and height are consistent before calculating the volume of any object.