Martina is using a magnifying glass. The lens of the magnifying glass has a diameter of 14 centimeters. What is the lens's area?

Use 3.14 for ​𝜋. If necessary, round your answer to the nearest hundredth.


To find the area of the lens, we can treat the lens as a circle. The formula for the area of a circle is:

\[
A = \pi r^2
\]

Where:
- \( A \) is the area,
- \( \pi \) is approximately 3.14,
- \( r \) is the radius of the circle.

Given that the diameter of the lens is 14 cm, the radius \( r \) is half the diameter:

\[
r = \frac{14}{2} = 7 \, \text{cm}
\]

Now, substitute \( r = 7 \, \text{cm} \) and \( \pi = 3.14 \) into the formula for the area:

\[
A = 3.14 \times 7^2 = 3.14 \times 49 = 153.86 \, \text{cm}^2
\]

Thus, the area of the lens is approximately \( 153.86 \, \text{cm}^2 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the area change if the diameter of the lens were doubled?
2. What is the formula for the circumference of a circle, and how would you apply it here?
3. If Martina had a second magnifying glass with a 10 cm diameter, what would its area be?
4. How does the area of a circle relate to its radius and diameter?
5. How would using a more accurate value of \( \pi \) affect the result?

**Tip:** Remember, the radius is always half of the diameter when dealing with circles.

Martina is using a magnifying glass. The lens of the magnifying glass has a diameter of 14 centimeters. What is the lens's area? Use 3.14 for ​𝜋. If necessary, round your answer to the nearest hundredth.

Calculate the area of a magnifying glass lens with a 14 cm diameter using the formula A = πr^2. With π approximated as 3.14, this problem illustrates key geometric concepts, making it perfect for students in Grades 6-8.

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