3-Real-Life Measurement:
• Choose an object from your surroundings (e.g.. a cylindrical bottle or a rectangular box). Measure its dimensions and calculate:
• Surface area
• Volume
• Write your calculations in the notebook and compare the results with the actual measurements.

Let's consider a common object, a **cylindrical bottle** as an example. To calculate its **surface area** and **volume**, we'll follow these steps:

### Measurements
Let's assume the following dimensions:
- Height (\( h \)) of the bottle = 20 cm
- Radius (\( r \)) of the bottle = 5 cm

### 1. Surface Area of the Cylinder
The surface area of a cylinder consists of:
- The lateral surface area, which is the side part of the cylinder.
- The top and bottom circular areas.

The formula for the **lateral surface area** is:
\[
A_{\text{lateral}} = 2 \pi r h
\]
The formula for the **area of the top and bottom** (two circles) is:
\[
A_{\text{circles}} = 2 \pi r^2
\]
Thus, the **total surface area** is:
\[
A_{\text{total}} = A_{\text{lateral}} + A_{\text{circles}} = 2 \pi r h + 2 \pi r^2 = 2 \pi r (h + r)
\]
Substitute the values:
\[
A_{\text{total}} = 2 \pi \times 5 \times (20 + 5) = 2 \pi \times 5 \times 25 = 250 \pi \, \text{cm}^2
\]
Approximating \(\pi \approx 3.1416\):
\[
A_{\text{total}} = 250 \times 3.1416 \approx 785.4 \, \text{cm}^2
\]

### 2. Volume of the Cylinder
The formula for the volume of a cylinder is:
\[
V = \pi r^2 h
\]
Substitute the values:
\[
V = \pi \times 5^2 \times 20 = \pi \times 25 \times 20 = 500 \pi \, \text{cm}^3
\]
Approximating \(\pi \approx 3.1416\):
\[
V = 500 \times 3.1416 \approx 1570.8 \, \text{cm}^3
\]

### Conclusion:
- **Surface area** ≈ 785.4 cm²
- **Volume** ≈ 1570.8 cm³

### Comparison with Actual Measurements
You can measure your cylindrical object using a ruler or measuring tape and compare the actual dimensions with the results from these formulas. Slight variations can occur due to measurement rounding or the accuracy of your tools.

Do you have an object in mind, or should I help with another example?

### Questions to explore:
1. How would the surface area change if the radius were doubled?
2. What happens to the volume if the height is halved but the radius remains the same?
3. Can you find the surface area of an open cylinder (no top)?
4. How does the surface area formula differ for a rectangular box?
5. What is the relationship between volume and surface area for different shapes?

### Tip:
Always double-check measurements using consistent units, such as cm or inches, for accuracy in real-life applications!

Choose an object from your surroundings (e.g., a cylindrical bottle or a rectangular box). Measure its dimensions and calculate: Surface area, Volume, and Compare the results with actual measurements.

Learn how to calculate the surface area and volume of a cylindrical bottle. This guide walks through measuring real-life objects, applying geometry formulas, and comparing results. Perfect for students in Grades 6-8 studying geometry and measurement.

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