https://file.aiquickdraw.com/mathbot/file/1727596187342d2rrs3rk.jpg

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.

A rectangular prism has length l cm, width w cm, and height h cm. Write an expression for the capacity of the container measured in different units. Similarly, a rectangular prism has length l m, width w m, and height h m. Write an expression for the capacity in various units.

Explore how to calculate the volume of a rectangular prism and convert between units such as cubic centimeters, liters, milliliters, and kiloliters. This problem covers important geometry concepts and unit conversions suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation