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This question asks about the largest possible sphere that can fit inside a cylinder with a height of 5 cm and a volume of 20 cm³.

The first step is to find the radius of the cylinder. The formula for the volume of a cylinder is:

\[
V = \pi r^2 h
\]

Where:
- \( V = 20 \, \text{cm}^3 \) (volume of the cylinder),
- \( h = 5 \, \text{cm} \) (height of the cylinder),
- \( r \) is the radius of the base of the cylinder, which we need to find.

Using the formula, we can solve for \( r \):

\[
20 = \pi r^2 \cdot 5
\]

Simplifying the equation:

\[
r^2 = \frac{20}{5\pi} = \frac{4}{\pi}
\]

Now, we take the square root:

\[
r = \sqrt{\frac{4}{\pi}} \approx \sqrt{1.27} \approx 1.13 \, \text{cm}
\]

This gives us the radius of the base of the cylinder.

Next, for the largest sphere that can fit inside the cylinder, the diameter of the sphere must be equal to the diameter of the cylinder, which is \( 2r \). So, the diameter of the largest sphere is:

\[
2r = 2 \times 1.13 \approx 2.26 \, \text{cm}
\]

To find the surface area of this sphere, we use the formula for the surface area of a sphere:

\[
A = 4\pi r^2
\]

Substituting \( r \approx 1.13 \):

\[
A \approx 4\pi (1.13)^2 \approx 4\pi \times 1.27 \approx 16.0 \, \text{cm}^2
\]

So, the largest possible surface area of a sphere that can fit inside this cylinder is approximately 16 cm².

Thus, the correct answer is **c. 16**.

Let me know if you need further details or explanations!

### Follow-up questions:
1. How would the answer change if the height of the cylinder were different?
2. Can the volume of the cylinder help determine the radius directly without finding the surface area?
3. What happens if the sphere’s radius exceeds the cylinder’s radius?
4. How can you calculate the volume of the sphere that fits inside the cylinder?
5. What other geometrical shapes can fit inside a cylinder besides spheres?

### Tip:
Remember, when dealing with cylinders and spheres, make sure to distinguish between their dimensions carefully, especially when calculating surface areas or volumes!

Sebuah silinder memiliki tinggi 5 cm dan volume 20 cm³. Luas permukaan bola terbesar yang mungkin diletakkan ke dalam silinder tersebut adalah...

Find the largest possible sphere that can fit inside a cylinder with a height of 5 cm and a volume of 20 cm³. Step-by-step solution with formulas for volume and surface area calculations. Suitable for high school students.

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