Here’s the breakdown of the exercises visible in the image:

Exercise 1: Conversion

You are required to convert between different units of volume:

1. 4.8 m³ to dm³
   1 m³ = 1000 dm³.
   So, $4.8 \, \text{m}^3 = 4.8 \times 1000 = 4800 \, \text{dm}^3$.

2. 764 dm³ to m³
   1 m³ = 1000 dm³.
   So, $764 \, \text{dm}^3 = \frac{764}{1000} = 0.764 \, \text{m}^3$.

3. 500 cm³ to dl
   1 cm³ = 0.01 dl.
   So, $500 \, \text{cm}^3 = 500 \times 0.01 = 5 \, \text{dl}$.

4. 0.48 dm³ to cl
   1 dm³ = 100 cl.
   So, $0.48 \, \text{dm}^3 = 0.48 \times 100 = 48 \, \text{cl}$.

Exercise 2: Volume of a rectangular prism

You are given dimensions:
22.5 mm, 18 mm, and 11.3 mm.

The formula for volume:
$V = \text{length} \times \text{width} \times \text{height}$

Converting to cm for easier interpretation:

• $22.5 \, \text{mm} = 2.25 \, \text{cm}$
• $18 \, \text{mm} = 1.8 \, \text{cm}$
• $11.3 \, \text{mm} = 1.13 \, \text{cm}$

$V = 2.25 \times 1.8 \times 1.13 = 4.57965 \, \text{cm}^3$

So, the volume is approximately $4.58 \, \text{cm}^3$.

Exercise 3: Volume of a cylinder

You are tasked with finding the capacity of a cylindrical box with:

• Diameter = 12 cm (thus, radius $r = \frac{12}{2} = 6 \, \text{cm}$),
• Height = 14 cm.

The formula for the volume of a cylinder: $V = \pi r^2 h$

Substituting: $V = \pi (6)^2 (14) = \pi (36) (14) = 504\pi \, \text{cm}^3$

Using $\pi \approx 3.1416$: $V \approx 504 \times 3.1416 = 1584.74 \, \text{cm}^3$

The capacity of the cylinder is approximately $1584.74 \, \text{cm}^3$.

Do you want detailed steps for any of these calculations or assistance with further examples?

Five Related Questions

1. How can you quickly convert between cubic meters and liters?
2. What are some practical applications of calculating cylinder volume in real life?
3. Can you explain the differences between volume units such as dl and cl?
4. Why is it important to standardize units before performing calculations?
5. How can you visualize the dimensions of a rectangular prism when given in millimeters?

Tip: Always ensure unit consistency in calculations by converting all measurements to the same unit system before solving.