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.