A can of beans has a height of 12 cm and a diameter of 7.6 cm. If you were to use the label that surrounds the can for advertising, how much surface area would you have to advertise on?

To find the surface area of the label that surrounds the can of beans, we need to calculate the lateral surface area of the cylinder.

Given:
- Height of the can \( h = 12 \, \text{cm} \)
- Diameter of the can \( d = 7.6 \, \text{cm} \)

First, we find the radius \( r \) of the can:
\[ r = \frac{d}{2} = \frac{7.6 \, \text{cm}}{2} = 3.8 \, \text{cm} \]

The lateral surface area \( A \) of a cylinder is given by the formula:
\[ A = 2 \pi r h \]

Substitute the given values:
\[ A = 2 \pi \times 3.8 \, \text{cm} \times 12 \, \text{cm} \]

Perform the multiplication:
\[ A = 2 \pi \times 3.8 \times 12 \]
\[ A = 2 \pi \times 45.6 \]
\[ A = 91.2 \pi \, \text{cm}^2 \]

Using the value of \(\pi \approx 3.14159\):
\[ A \approx 91.2 \times 3.14159 \]
\[ A \approx 286.48 \, \text{cm}^2 \]

Therefore, the surface area available for advertising on the label is approximately \( \boxed{286.48 \, \text{cm}^2} \).

Would you like any further details or have any questions?

Here are 5 questions you can ask:
1. How do you calculate the volume of a cone?
2. What is the formula for the surface area of a sphere?
3. How do you solve systems of linear equations?
4. Can you explain the concept of limits in calculus?
5. How do you find the area of a trapezoid?

**Tip:** Always double-check the units and conversion factors when performing calculations to ensure accuracy.

Discover how to calculate the surface area of a cylinder with a practical example involving a can of beans. Learn the formula A = 2πrh and compute the advertising space available on the can's label. Suitable for students in Grades 7-9.

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