Answer :
To calculate the volume of a sphere, we use the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where [tex]\( V \)[/tex] is the volume and [tex]\( r \)[/tex] is the radius of the sphere. In this case, the radius [tex]\( r \)[/tex] is given as 2.5 meters.
Let's break down the steps:
1. Determine the radius: The given radius is 2.5 meters.
2. Cube the radius: We need to compute [tex]\( r^3 \)[/tex], which is:
[tex]\[ (2.5)^3 = 2.5 \times 2.5 \times 2.5 = 15.625 \][/tex]
3. Multiply by π: Using the value [tex]\( \pi \approx 3.141592653589793 \)[/tex], we multiply:
[tex]\[ \pi \times 15.625 \approx 3.141592653589793 \times 15.625 = 49.087385212340516 \][/tex]
4. Calculate the final volume using the formula: We need to multiply by [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[ V = \frac{4}{3} \times \pi \times r^3 = \frac{4}{3} \times 49.087385212340516 = 65.44984694978736 \][/tex]
Thus, the volume of the sphere with a radius of 2.5 meters is approximately [tex]\( 65.45 \, \text{m}^3 \)[/tex].
So, the correct answer is:
[tex]\[65.45 \, m^3 \][/tex]
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where [tex]\( V \)[/tex] is the volume and [tex]\( r \)[/tex] is the radius of the sphere. In this case, the radius [tex]\( r \)[/tex] is given as 2.5 meters.
Let's break down the steps:
1. Determine the radius: The given radius is 2.5 meters.
2. Cube the radius: We need to compute [tex]\( r^3 \)[/tex], which is:
[tex]\[ (2.5)^3 = 2.5 \times 2.5 \times 2.5 = 15.625 \][/tex]
3. Multiply by π: Using the value [tex]\( \pi \approx 3.141592653589793 \)[/tex], we multiply:
[tex]\[ \pi \times 15.625 \approx 3.141592653589793 \times 15.625 = 49.087385212340516 \][/tex]
4. Calculate the final volume using the formula: We need to multiply by [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[ V = \frac{4}{3} \times \pi \times r^3 = \frac{4}{3} \times 49.087385212340516 = 65.44984694978736 \][/tex]
Thus, the volume of the sphere with a radius of 2.5 meters is approximately [tex]\( 65.45 \, \text{m}^3 \)[/tex].
So, the correct answer is:
[tex]\[65.45 \, m^3 \][/tex]
