Sure! Let's solve this step by step.
### Step 1: Understand the relationship between diameter and radius
The radius of a sphere is half of its diameter.
Given:
- Diameter ([tex]\(d\)[/tex]) = 6 cm
- Radius ([tex]\(r\)[/tex]) = [tex]\( \frac{d}{2} \)[/tex] = [tex]\( \frac{6}{2} \)[/tex] = 3 cm
### Step 2: Utilize the formula for the volume of a sphere
The volume [tex]\(V\)[/tex] of a sphere is given by the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
### Step 3: Substitute the values for [tex]\(\pi\)[/tex] and [tex]\(r\)[/tex] into the formula
Given [tex]\(\pi \approx 3.14\)[/tex] and [tex]\(r = 3\)[/tex] cm, we plug these values into the formula:
[tex]\[ V = \frac{4}{3} \cdot 3.14 \cdot (3^3) \][/tex]
### Step 4: Calculate the cube of the radius
First, calculate [tex]\(3^3\)[/tex]:
[tex]\[ 3^3 = 3 \times 3 \times 3 = 27 \][/tex]
### Step 5: Substitute and simplify
[tex]\[ V = \frac{4}{3} \cdot 3.14 \cdot 27 \][/tex]
### Step 6: Calculate the multiplication and division
First, calculate [tex]\(\frac{4}{3} \times 27\)[/tex]:
[tex]\[ \frac{4}{3} \times 27 = 4 \times 9 = 36 \][/tex]
Next, multiply by [tex]\(\pi\)[/tex]:
[tex]\[ V = 36 \times 3.14 = 113.04 \][/tex]
### Step 7: State the final volume
The volume of the ball is:
[tex]\[ V \approx 113.04 \text{ cm}^3 \][/tex]
Therefore, the volume of a ball with a diameter of 6 centimeters is approximately 113.04 cubic centimeters when using 3.14 for [tex]\(\pi\)[/tex].
