What is the volume of a sphere with a radius of 4.0830 m?

To determine the volume of a sphere, you can use the formula:

[

V = \frac{4}{3} \pi r^3

]

where ( V ) is the volume and ( r ) is the radius of the sphere.

In this case, the radius ( r ) is given as 4.0830 meters. First, calculate the cube of the radius:

[

r^3 = (4.0830)^3 \approx 68.2441 , \text{m}^3

]

Next, multiply this by ( \pi ) (approximately 3.14159):

[

\pi r^3 \approx 3.14159 \times 68.2441 \approx 214.395 , \text{m}^3

]

Now, multiply that result by ( \frac{4}{3} ):

[

V \approx \frac{4}{3} \times 214.395 \approx 285.12 , \text{m}^3

]

This volume matches the answer labeled as option C, confirming that the calculation is accurate. The formula and the steps taken illustrate how units