Answer :
To calculate the volume of a sphere given the radius, we can use the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the sphere,
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14,
- [tex]\( r \)[/tex] is the radius of the sphere.
Given:
- Radius [tex]\( r = 5.4 \, \text{m} \)[/tex]
- [tex]\( \pi = 3.14 \)[/tex]
Let's break down the calculation step-by-step.
1. Calculate the cube of the radius:
[tex]\[ r^3 = (5.4)^3 \][/tex]
[tex]\[ r^3 = 5.4 \times 5.4 \times 5.4 \][/tex]
[tex]\[ r^3 = 157.464 \][/tex]
2. Multiply the result by [tex]\(\pi\)[/tex]:
[tex]\[ \pi r^3 = 3.14 \times 157.464 \][/tex]
[tex]\[ \pi r^3 = 494.43336 \][/tex]
3. Multiply by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
[tex]\[ V = \frac{4}{3} \times 494.43336 \][/tex]
[tex]\[ V = 659.2492800000001 \][/tex]
So, the exact volume calculated is [tex]\( 659.2492800000001 \, \text{m}^3 \)[/tex].
4. Round the result to the nearest tenth:
[tex]\[ V \approx 659.2 \, \text{m}^3 \][/tex]
The volume of the sphere, rounded to the nearest tenth, is [tex]\( 659.2 \, \text{m}^3 \)[/tex].
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the sphere,
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14,
- [tex]\( r \)[/tex] is the radius of the sphere.
Given:
- Radius [tex]\( r = 5.4 \, \text{m} \)[/tex]
- [tex]\( \pi = 3.14 \)[/tex]
Let's break down the calculation step-by-step.
1. Calculate the cube of the radius:
[tex]\[ r^3 = (5.4)^3 \][/tex]
[tex]\[ r^3 = 5.4 \times 5.4 \times 5.4 \][/tex]
[tex]\[ r^3 = 157.464 \][/tex]
2. Multiply the result by [tex]\(\pi\)[/tex]:
[tex]\[ \pi r^3 = 3.14 \times 157.464 \][/tex]
[tex]\[ \pi r^3 = 494.43336 \][/tex]
3. Multiply by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
[tex]\[ V = \frac{4}{3} \times 494.43336 \][/tex]
[tex]\[ V = 659.2492800000001 \][/tex]
So, the exact volume calculated is [tex]\( 659.2492800000001 \, \text{m}^3 \)[/tex].
4. Round the result to the nearest tenth:
[tex]\[ V \approx 659.2 \, \text{m}^3 \][/tex]
The volume of the sphere, rounded to the nearest tenth, is [tex]\( 659.2 \, \text{m}^3 \)[/tex].
