https://file.aiquickdraw.com/mathbot/file/1729333144857cstzsgh3.jpg

To find the area of the shaded face of the cylinder, which is the top circular face, you can use the formula for the area of a circle:

\[
A = \pi r^2
\]

Where:
- \(A\) is the area of the circle.
- \(r\) is the radius of the circle.
- \(\pi\) is approximately 3.14159.

From the image, the diameter of the circle is given as 26 mm, so the radius \(r\) is half of the diameter:

\[
r = \frac{26}{2} = 13 \, \text{mm}
\]

Now, plug the radius into the area formula:

\[
A = \pi (13)^2 = \pi \times 169 \approx 3.14159 \times 169 = 531.9 \, \text{mm}^2
\]

Rounding to the nearest whole number, the area is approximately:

\[
A \approx 532 \, \text{mm}^2
\]

Thus, the area of the shaded face of the cylinder is **532 mm²**.

Would you like more details or have any questions? Here are five related questions to expand on this topic:

1. What would happen to the area if the diameter were doubled?
2. How do you calculate the surface area of the entire cylinder?
3. What is the difference between diameter and radius in any circle?
4. How would the area change if the unit was in centimeters instead of millimeters?
5. Can the area formula be used for non-circular shapes?

**Tip:** Always ensure you correctly identify the radius (half of the diameter) when solving area problems involving circles.

What is the area of the shaded face of this cylinder?

Learn how to find the area of the shaded circular face of a cylinder with a diameter of 26 mm. This problem involves basic geometry concepts and the formula A = πr^2. Suitable for students in Grades 5-6.

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