https://file.aiquickdraw.com/mathbot/file/17304996221437gjkm9xt.jpg

The problem is asking for the volume of a sphere with a radius of 12 cm, using 3.14 for \(\pi\) and rounding to the nearest hundredth.

The formula for the volume \(V\) of a sphere is:
\[
V = \frac{4}{3} \pi r^3
\]
where \(r\) is the radius.

### Step-by-Step Solution
1. Substitute the given values:
   - \(r = 12\) cm
   - \(\pi = 3.14\)

2. Substitute these values into the formula:
   \[
   V = \frac{4}{3} \times 3.14 \times (12)^3
   \]

3. Calculate \(12^3\):
   \[
   12^3 = 1728
   \]

4. Multiply by \(\pi\):
   \[
   3.14 \times 1728 = 5425.92
   \]

5. Multiply by \(\frac{4}{3}\):
   \[
   V = \frac{4}{3} \times 5425.92 = 7234.56 \text{ cm}^3
   \]

### Answer
The volume of the sphere is approximately:
\[
7234.56 \, \text{cm}^3
\]

Would you like further details or have any questions?

### Related Questions
1. How would the volume change if the radius were doubled?
2. What is the surface area of a sphere with the same radius?
3. How would the formula for volume differ for a hemisphere?
4. If \(\pi\) were approximated to a different value, how would it affect the volume?
5. Can the volume formula for a sphere be derived using integration?

### Tip
Remember, when working with powers, ensure that all multiplications are accurate to avoid rounding errors in intermediate steps.

Find the volume of a sphere with a radius of 12 cm, using 3.14 for π and rounding to the nearest hundredth.

Learn how to calculate the volume of a sphere with a radius of 12 cm using the formula V = (4/3)πr³. This solution uses 3.14 for π and provides a step-by-step calculation, rounded to the nearest hundredth. Suitable for students in Grades 9-11.

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