https://file.aiquickdraw.com/mathbot/file/1726001247654s0w7uhvd.jpg

Let's go through each shape and calculate their volumes, rounding the answers to 1 decimal place as requested.

1. **Cylinder 1** (Height = 6 cm, Diameter = 4 cm)
   - Formula: \( V = \pi r^2 h \)
   - Radius \( r = \frac{4}{2} = 2 \) cm
   - Height \( h = 6 \) cm

   Volume \( V = \pi (2)^2(6) = 24\pi \approx 75.4 \, \text{cm}^3 \)

2. **Cylinder 2** (Height = 7 cm, Diameter = 4.2 cm)
   - Formula: \( V = \pi r^2 h \)
   - Radius \( r = \frac{4.2}{2} = 2.1 \) cm
   - Height \( h = 7 \) cm

   Volume \( V = \pi (2.1)^2(7) = 30.87\pi \approx 97.0 \, \text{cm}^3 \)

3. **Half-Cylinder** (Length = 30 cm, Radius = 12 cm)
   - Formula for full cylinder: \( V = \pi r^2 h \)
   - Radius \( r = 12 \) cm, Length \( h = 30 \) cm
   - Full volume \( V = \pi (12)^2 (30) = 4320\pi \)
   - Since it's half-cylinder, divide by 2: 
   
   Volume \( V = \frac{4320\pi}{2} \approx 6785.8 \, \text{cm}^3 \)

4. **Pipe** (Length = 25 cm, Internal diameter = 5 cm, Thickness = 0.5 cm)
   - Inner radius \( r_1 = \frac{5}{2} = 2.5 \) cm
   - Outer radius \( r_2 = 2.5 + 0.5 = 3 \) cm
   - Formula: \( V = \pi (r_2^2 - r_1^2) h \)
   - Height \( h = 25 \) cm

   Volume \( V = \pi \left(3^2 - 2.5^2\right)(25) = \pi (9 - 6.25)(25) = 68.75\pi \approx 216 \, \text{cm}^3 \)

So, the volumes are:

1. \( 75.4 \, \text{cm}^3 \)
2. \( 97.0 \, \text{cm}^3 \)
3. \( 6785.8 \, \text{cm}^3 \)
4. \( 216 \, \text{cm}^3 \)

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the formula for the surface area of a cylinder?
2. How does the volume of a cone compare to the volume of a cylinder with the same base and height?
3. How do you calculate the volume of a hollow sphere?
4. What is the significance of using the \( \pi \) button in volume calculations?
5. How would the volume change if the thickness of the pipe increased by 1 cm?

**Tip:** Always make sure the units are consistent before plugging them into formulas, especially when working with different shapes and conversions.

Work out the volume of each solid using the π button on your calculator. Calculate the volumes for a cylinder, a half-cylinder, and a pipe.

Learn how to calculate the volumes of cylinders, half-cylinders, and pipes using the formula V = πr²h. This problem involves solid geometry and is suitable for students in Grades 8-10, covering key concepts such as the use of π in geometric formulas.

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