Question

You buy a can of soup and decide to replace the label with your own. If the radius of the can is 4.5cm, what is the length of the label?

Answer 1

The length of the label needed to replace on a soup can with a radius of 4.5 cm is approximately 28.27 cm, which is the circumference of the can.

Step-by-step explanation:

To find the length of the label that will replace the existing one on a soup can, we need to calculate the circumference of the circular cross-section of the can since the label wraps around that circumference. The formula for the circumference (C) of a circle is C = 2πr, where π is approximately 3.14159, and r is the radius of the circle.

Given that the radius of the can is 4.5 cm, the calculation is as follows:
C = 2π(4.5 cm) = 2 × 3.14159 × 4.5 cm = 28.274 cm

So the length of the label that you would need to create to fully wrap around the can is approximately 28.27 cm, given that π is a transcendental number and the value of the circumference should be rounded to match the significant figures of the given radius, which is two significant figures.

Answer 2

The length of the label for the can of soup with a radius of 4.5 cm is approximately 28.27 cm.

Explanation:

When replacing the label on a can, the length of the label corresponds to the circumference of the can. The formula for the circumference (C) of a circle is given by C = 2πr, where r is the radius of the circle. In this case, the radius (r) is 4.5 cm.

Now, substitute the given value into the formula:

`\[ C = 2π * 4.5 \]`

Calculate the circumference:

`\[ C ≈ 2 * 3.14 * 4.5 \]`

`\[ C ≈ 28.27 \]`

Therefore, the length of the label required for the can with a radius of 4.5 cm is approximately 28.27 cm. This value represents the distance around the can, and by placing a label of this length, you can fully cover the circumference of the can.

In summary, when changing the label on a can, it's crucial to use the circumference formula to determine the correct length. In this case, the radius of the can was provided, and by applying the formula, we found that a label with a length of approximately 28.27 cm is needed to fully encircle the can. This ensures a proper fit and coverage for the replaced label.