https://file.aiquickdraw.com/mathbot/file/1726724296248w9wnw7pp.jpg

The given image shows a solid cylinder, and the question is asking for its surface area. The radius of the base of the cylinder is given as \( r = 4 \), and the height of the cylinder is \( h = 6 \).

To find the surface area \( A \) of a cylinder, we use the formula:

\[
A = 2\pi r^2 + 2\pi r h
\]

Where:
- \( 2\pi r^2 \) is the area of the two circular bases (top and bottom),
- \( 2\pi r h \) is the area of the lateral surface (the curved side).

### Step-by-Step Calculation:

1. **Area of the two bases**:
   \[
   2\pi r^2 = 2\pi (4)^2 = 2\pi \times 16 = 32\pi
   \]

2. **Area of the lateral surface**:
   \[
   2\pi r h = 2\pi \times 4 \times 6 = 48\pi
   \]

3. **Total Surface Area**:
   \[
   A = 32\pi + 48\pi = 80\pi
   \]

Thus, the surface area of the cylinder is \( 80\pi \), but since this isn't listed among the provided answer choices, the correct response is **E. NOTA (None of the Above)**.

Would you like further clarification or have any additional questions?

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Here are 5 related questions:
1. How would you calculate the volume of this cylinder?
2. What happens to the surface area if the radius doubles?
3. How do you calculate the surface area of other 3D shapes like cones or spheres?
4. What is the lateral surface area of the cylinder alone?
5. What is the effect of increasing the height on the surface area?

**Tip:** Always distinguish between surface area and volume formulas when working with 3D shapes.

What is the surface area of the solid below? The solid is a cylinder with a radius of 4 and height of 6.

Calculate the surface area of a cylinder with a radius of 4 and height of 6. This detailed solution covers geometric concepts such as the surface area of 3D shapes, with a step-by-step breakdown of the calculations using the surface area formula for cylinders. Suitable for students in Grades 8-10.

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