94.25
245.04
188.50
603.19
376.99
A can of peaches has a diameter of 6
centimeters and a height of 10
centimeters.

Use the options to complete the sentence.

The can of peaches requires  square centimeters of paper to create the label for the can, and  square centimeters of metal to make the can.

To answer this question, let's calculate the surface area of the can for both the label and the entire can.

### Given Data
- **Diameter of the can** \( = 6 \) cm, so **radius** \( r = \frac{6}{2} = 3 \) cm.
- **Height of the can** \( h = 10 \) cm.

### 1. Surface Area for the Label
The label typically covers only the curved surface area of the can. The formula for the lateral (curved) surface area of a cylinder is:
\[
\text{Lateral Surface Area} = 2 \pi r h
\]
Substituting in the values:
\[
= 2 \pi (3) (10) = 60 \pi \approx 188.4 \text{ square centimeters}
\]

So, **the can requires approximately 188.4 square centimeters of paper** to create the label.

### 2. Total Surface Area for the Metal Can
To find the total surface area (metal needed), we need to consider both the curved surface and the two circular bases (top and bottom). The formula for the total surface area of a cylinder is:
\[
\text{Total Surface Area} = 2 \pi r h + 2 \pi r^2
\]
Substituting in the values:
\[
= 2 \pi (3) (10) + 2 \pi (3)^2
\]
\[
= 60 \pi + 18 \pi = 78 \pi \approx 245.0 \text{ square centimeters}
\]

So, **the can requires approximately 245.0 square centimeters of metal** to make the can.

### Final Answer
The can of peaches requires **188.4 square centimeters** of paper for the label and **245.0 square centimeters** of metal to make the can.

Would you like further details or have any questions?

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#### Related Questions:
1. How would these calculations change if the height of the can increased?
2. How is the surface area of a can affected if the radius is doubled?
3. What is the difference between lateral surface area and total surface area?
4. How could these surface area calculations be applied to a real-world packaging scenario?
5. Why is the curved surface area used for the label rather than the total surface area?

#### Tip:
When working with cylinders, always identify which parts (curved or total) are required to avoid overestimating or underestimating material needs.

A can of peaches has a diameter of 6 centimeters and a height of 10 centimeters. Use the options to complete the sentence. The can of peaches requires square centimeters of paper to create the label for the can, and square centimeters of metal to make the can.

Calculate the paper and metal required for a cylindrical can of peaches with a diameter of 6 cm and height of 10 cm. Explore how to find the lateral surface area for labeling and the total surface area for metal needs, using cylinder surface area formulas. Suitable for Grades 6-8.

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