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