The diameter of a sphere is 10 cm. What is the sphere's volume? Round to the nearest tenth.

1 answer

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.