Answer :
To find the volume of a sphere with a radius of 30 units, we can use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the sphere,
- [tex]\( r \)[/tex] is the radius of the sphere,
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
Given that the radius [tex]\( r \)[/tex] is 30 units, substituting this value into the formula gives:
[tex]\[ V = \frac{4}{3} \pi (30)^3 \][/tex]
First, we need to calculate the cube of the radius:
[tex]\[ 30^3 = 27,000 \][/tex]
Next, plug this value back into the formula:
[tex]\[ V = \frac{4}{3} \pi \times 27,000 \][/tex]
Now, multiplying the constant factors:
[tex]\[ \frac{4}{3} \pi \times 27,000 = \frac{4 \times 27,000}{3} \pi \][/tex]
[tex]\[ \frac{108,000}{3} \pi = 36,000 \pi \][/tex]
Finally, multiplying by [tex]\( \pi \)[/tex] to get the volume:
[tex]\[ V \approx 36,000 \times 3.14159 = 113097.33552923254 \][/tex]
Therefore, the volume of the sphere is approximately [tex]\( 113,097 \)[/tex] units³, which is closest to none of the given options. Thus, there might be an error in the provided options or a misunderstanding, but provided calculations are correct. The closest integer value to the previously computed volume is:
[tex]\[ 113,097 \text{ units}^3 \][/tex]
Here is the volume correctly calculated with all appropriate steps.
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the sphere,
- [tex]\( r \)[/tex] is the radius of the sphere,
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
Given that the radius [tex]\( r \)[/tex] is 30 units, substituting this value into the formula gives:
[tex]\[ V = \frac{4}{3} \pi (30)^3 \][/tex]
First, we need to calculate the cube of the radius:
[tex]\[ 30^3 = 27,000 \][/tex]
Next, plug this value back into the formula:
[tex]\[ V = \frac{4}{3} \pi \times 27,000 \][/tex]
Now, multiplying the constant factors:
[tex]\[ \frac{4}{3} \pi \times 27,000 = \frac{4 \times 27,000}{3} \pi \][/tex]
[tex]\[ \frac{108,000}{3} \pi = 36,000 \pi \][/tex]
Finally, multiplying by [tex]\( \pi \)[/tex] to get the volume:
[tex]\[ V \approx 36,000 \times 3.14159 = 113097.33552923254 \][/tex]
Therefore, the volume of the sphere is approximately [tex]\( 113,097 \)[/tex] units³, which is closest to none of the given options. Thus, there might be an error in the provided options or a misunderstanding, but provided calculations are correct. The closest integer value to the previously computed volume is:
[tex]\[ 113,097 \text{ units}^3 \][/tex]
Here is the volume correctly calculated with all appropriate steps.
