What is the approximate volume of a sphere with a radius of 5 m?

What is the approximate volume of a sphere with a radius of 5 m?

• A. 523.6
• B. 209.2
• C. 1,047.2
• D. 1,047.9

Answer: (C)

To determine the volume of a sphere, the formula used is \( V = \frac{4}{3} \pi r^3 \), where \( r \) is the radius of the sphere. In this case, the radius is given as 5 meters. Substituting the radius into the formula, we calculate the volume as follows: 1. Calculate \( r^3 = 5^3 = 125 \). 2. Multiply by \( \pi \) (approximately 3.14159), and then by \( \frac{4}{3} \): \[ V = \frac{4}{3} \pi (125) \approx \frac{4}{3} \times 3.14159 \times 125 \approx 523.598 \, m^3 \] When rounded, this value is approximately 523.6 m³. This calculation shows that the volume of the sphere in question is indeed around 523.6 m³, confirming the correctness of the choice. By contrast, other provided options come from different calculations or misunderstandings of the volume formula, leading to values that don't align with the actual computation based on the given radius. Thus,

To determine the volume of a sphere, the formula used is ( V = \frac{4}{3} \pi r^3 ), where ( r ) is the radius of the sphere. In this case, the radius is given as 5 meters.

Substituting the radius into the formula, we calculate the volume as follows:

1. Calculate ( r^3 = 5^3 = 125 ).

2. Multiply by ( \pi ) (approximately 3.14159), and then by ( \frac{4}{3} ):

[

V = \frac{4}{3} \pi (125) \approx \frac{4}{3} \times 3.14159 \times 125 \approx 523.598 , m^3

]

When rounded, this value is approximately 523.6 m³.

This calculation shows that the volume of the sphere in question is indeed around 523.6 m³, confirming the correctness of the choice.

By contrast, other provided options come from different calculations or misunderstandings of the volume formula, leading to values that don't align with the actual computation based on the given radius. Thus,