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This problem describes a cylindrical water tank with a height of 1 meter and a volume of 0.4 cubic meters. We are tasked with finding the radius of the base of the cylinder.

The formula for the volume of a cylinder is:

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

Where:
- \( V \) is the volume (0.4 m³),
- \( r \) is the radius of the base,
- \( h \) is the height (1 meter),
- \( \pi \) is approximately 3.1416.

### Step-by-step solution:

1. Substitute the known values into the volume formula:

\[
0.4 = \pi r^2 \times 1
\]

2. Simplify the equation:

\[
0.4 = \pi r^2
\]

3. Solve for \( r^2 \):

\[
r^2 = \frac{0.4}{\pi}
\]

4. Take the square root of both sides:

\[
r = \sqrt{\frac{0.4}{\pi}}
\]

So, the radius \( r \) is \( \sqrt{\frac{0.4}{\pi}} \).

Looking at the options provided in the image, option **B** \( \frac{0.4}{\pi} \) is not quite correct, but **D** \( \sqrt{\frac{0.4}{\pi}} \) matches the correct format.

Thus, the correct answer is **D**.

Would you like more details on this solution or help with another question?

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### 5 Related Questions:
1. What is the formula for the surface area of a cylinder?
2. How would the radius change if the height were doubled?
3. What would happen to the volume if the radius doubled but the height remained the same?
4. How can you calculate the height if the radius and volume are known?
5. What is the relationship between the volume of a sphere and the volume of a cylinder?

### Tip:
When solving geometry problems involving circles or cylinders, always remember to correctly substitute the values into formulas and keep track of the units to avoid errors.

Uma indústria planeja produzir caixa-d'água, em formato cilíndrico, com 1 m de altura, capaz de armazenar 0,4 m³ de água. A medida do raio da base dessa caixa-d'água, em metro, deve ser?

Learn how to calculate the radius of a cylindrical water tank with a height of 1 meter and a volume of 0.4 cubic meters. This problem uses the formula for the volume of a cylinder (V = πr²h) and involves solving for the radius by extracting square roots.

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