To find the difference in volumes between a softball and a baseball, we will first calculate the volumes of each using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
Step 1: Calculate the volume of the softball
- The diameter of the softball is 3.5 inches; thus, the radius \( r \) is: \[ r = \frac{3.5}{2} = 1.75 \text{ inches} \]
- Now, use the volume formula: \[ V_{\text{softball}} = \frac{4}{3} \pi (1.75)^3 \] Calculating \( (1.75)^3 \): \[ (1.75)^3 = 5.359375 \] Now substitute into the volume formula: \[ V_{\text{softball}} = \frac{4}{3} \cdot 3.14 \cdot 5.359375 \] \[ = \frac{4 \cdot 3.14 \cdot 5.359375}{3} \approx \frac{67.539 \text{ in}^3}{3} \approx 22.5 \text{ in}^3 \]
Step 2: Calculate the volume of the baseball
- The diameter of the baseball is 2.9 inches; thus, the radius \( r \) is: \[ r = \frac{2.9}{2} = 1.45 \text{ inches} \]
- Now, use the volume formula: \[ V_{\text{baseball}} = \frac{4}{3} \pi (1.45)^3 \] Calculating \( (1.45)^3 \): \[ (1.45)^3 = 3.073125 \] Now substitute into the volume formula: \[ V_{\text{baseball}} = \frac{4}{3} \cdot 3.14 \cdot 3.073125 \] \[ = \frac{4 \cdot 3.14 \cdot 3.073125}{3} \approx \frac{38.513 \text{ in}^3}{3} \approx 12.8 \text{ in}^3 \]
Step 3: Calculate the difference in volumes
Now subtract the volume of the baseball from the volume of the softball: \[ \text{Difference} = V_{\text{softball}} - V_{\text{baseball}} \] \[ = 22.5 \text{ in}^3 - 12.8 \text{ in}^3 = 9.7 \text{ in}^3 \]
Step 4: Round the answer to the nearest tenth
The approximate difference in their volumes is: \[ \boxed{9.7 \text{ in}^3} \]