https://file.aiquickdraw.com/mathbot/file/1727595140108fqxkt2r8.jpg

Let's go through the questions in the image and solve them step by step.

### Question 15:

The problem asks to write expressions for \( x \) liters in different units, knowing that \( x \) liters equals 1000 \( x \) milliliters because there are 1000 mL in 1 L.

1. **15 a (i): cm³**  
   To convert liters to cubic centimeters (cm³):  
   1 liter \( = 1000 \, \text{cm}^3 \)  
   Therefore, \( x \) liters \( = 1000x \, \text{cm}^3 \).

2. **15 b (ii): m³**  
   To convert liters to cubic meters (m³):  
   1 liter \( = 0.001 \, \text{m}^3 \)  
   Therefore, \( x \) liters \( = 0.001x \, \text{m}^3 \).

3. **15 c (iii): kL**  
   To convert liters to kiloliters (kL):  
   1 kiloliter \( = 1000 \, \text{L} \),  
   So \( x \) liters \( = \frac{x}{1000} \, \text{kL} \).

4. **15 d (iv): mL**  
   To convert liters to milliliters (mL):  
   1 liter \( = 1000 \, \text{mL} \),  
   So \( x \) liters \( = 1000x \, \text{mL} \).

---

### Question 16:

This question asks for the volume of a rectangular prism with length \( l \), width \( w \), and height \( h \), expressed in different units.

1. **16 a (i): cm³**  
   The volume of a rectangular prism is given by \( V = l \times w \times h \) in cubic centimeters.  
   The expression for the volume in \( \text{cm}^3 \) is \( V = l \times w \times h \).

2. **16 b (ii): m³**  
   To express the volume in cubic meters, convert the dimensions from centimeters to meters:  
   1 cm = 0.01 m,  
   So the volume \( V = (l \times 0.01)(w \times 0.01)(h \times 0.01) \, \text{m}^3 \),  
   Simplifying, \( V = l \times w \times h \times 10^{-6} \, \text{m}^3 \).

3. **16 c (iii): L**  
   Since 1 liter \( = 1000 \, \text{cm}^3 \),  
   Volume in liters is \( V = \frac{l \times w \times h}{1000} \, \text{L} \).

4. **16 d (iv): kL**  
   To convert to kiloliters, knowing 1 kL = 1000 L:  
   \( V = \frac{l \times w \times h}{1000 \times 1000} = \frac{l \times w \times h}{1,000,000} \, \text{kL} \).

5. **16 e (v): mL**  
   Since 1 mL = 1 cm³,  
   The volume in milliliters is \( V = l \times w \times h \, \text{mL} \).

---

Would you like any further details on the calculations? Here are 5 related questions to think about:

1. How do you convert cubic meters to liters?
2. If you know the volume in kL, how would you convert that to cm³?
3. What is the difference between kiloliters and milliliters in terms of conversion?
4. How would you calculate the volume of a cylinder instead of a rectangular prism?
5. How does the conversion between units change if you're dealing with mass instead of volume?

**Tip:** Always remember to check unit consistency when performing volume calculations, especially when dimensions are provided in different units.

If x is any number, then x liters is the same as 1000x milliliters because there are 1000 mL in 1 L. Write expressions for x liters in the following units (cm³, m³, kL, mL) and determine the volume of a rectangular prism in various units (cm³, m³, L, kL, mL).

Solve problems involving the conversion of liters into cm³, m³, kL, and mL, and learn how to calculate the volume of a rectangular prism in different units. This guide is perfect for middle school students learning unit conversions and volume calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation