To find the volume of a sphere, we can use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere. Since the diameter of the sphere is 10 cm, the radius \( r \) is half of that:
\[ r = \frac{10 \text{ cm}}{2} = 5 \text{ cm} \]
Now, we can substitute the radius into the volume formula:
\[ V = \frac{4}{3} \pi (5 \text{ cm})^3 \]
Calculating \( (5 \text{ cm})^3 \):
\[ (5 \text{ cm})^3 = 125 \text{ cm}^3 \]
Now substituting this value back into the volume formula:
\[ V = \frac{4}{3} \pi (125 \text{ cm}^3) = \frac{500}{3} \pi \text{ cm}^3 \]
To approximate the value, we will use \( \pi \approx 3.14159 \):
\[ V \approx \frac{500}{3} \times 3.14159 \text{ cm}^3 \]
Calculating \( \frac{500}{3} \):
\[ \frac{500}{3} \approx 166.6667 \]
Now multiplying by \( \pi \):
\[ V \approx 166.6667 \times 3.14159 \approx 523.5983 \text{ cm}^3 \]
Rounding to the nearest tenth:
\[ V \approx 523.6 \text{ cm}^3 \]
Thus, the volume of the sphere is approximately 523.6 cm³.