To find the volume of a spherical ball with a diameter of 14 cm, we can break the problem into a few straightforward steps. We'll use the formula for the volume of a sphere, [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex], where [tex]\( r \)[/tex] is the radius.
### Step 1: Finding the Radius
The diameter of the sphere is given as 14 cm. The radius is half of the diameter:
[tex]\[
r = \frac{d}{2} = \frac{14}{2} = 7 \text{ cm}
\][/tex]
### Step 2: Apply the Volume Formula
The formula for the volume of a sphere is:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
Substitute [tex]\( r = 7 \)[/tex] cm and [tex]\( \pi = 3.14 \)[/tex]:
[tex]\[
V = \frac{4}{3} \times 3.14 \times 7^3
\][/tex]
### Step 3: Calculate [tex]\( r^3 \)[/tex]
First, calculate [tex]\( 7^3 \)[/tex]:
[tex]\[
7^3 = 7 \times 7 \times 7 = 343
\][/tex]
### Step 4: Plug the Values into the Formula
Now, substitute [tex]\( r^3 = 343 \)[/tex] into the volume formula:
[tex]\[
V = \frac{4}{3} \times 3.14 \times 343
\][/tex]
### Step 5: Simplify the Expression
Calculate the multiplication:
[tex]\[
\frac{4}{3} \times 3.14 = \frac{4 \times 3.14}{3} = \frac{12.56}{3} = 4.1866666666666665
\][/tex]
So,
[tex]\[
V \approx 4.1866666666666665 \times 343 \approx 1436.03 \text{ cm}^3
\][/tex]
### Step 6: Round to the Nearest Hundredth
The computed volume value is:
[tex]\[
1436.0266666666666 \text{ cm}^3
\][/tex]
Rounding this to the nearest hundredth, we get:
[tex]\[
1436.03 \text{ cm}^3
\][/tex]
### Conclusion
Therefore, the volume of the spherical ball with a diameter of 14 cm is approximately [tex]\( 1436.03 \, \text{cm}^3 \)[/tex].
The correct answer from the given choices is:
[tex]\[
1,436.03 \, \text{cm}^3
\][/tex]
