To find how much larger the volume calculation of a sphere is when using \( \pi \) compared to using \( 3.14 \), we'll calculate the volume of the sphere using both values.
The formula for the volume \( V \) of a sphere is:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
Step 1: Calculate the volume using \( \pi \)
Given:
- \( r = 39 \) inches
- Using \( \pi \):
\[ V_{\pi} = \frac{4}{3} \pi (39)^3 \]
Calculating \( 39^3 \):
\[ 39^3 = 39 \times 39 \times 39 = 59319 \]
Now substituting back into the volume formula:
\[ V_{\pi} = \frac{4}{3} \pi (59319) \approx \frac{4}{3} \times 3.14159 \times 59319 \approx 248998.293 \text{ cubic inches} \]
Step 2: Calculate the volume using \( 3.14 \)
Now, we use \( 3.14 \):
\[ V_{3.14} = \frac{4}{3} (3.14) (39)^3 \]
Using \( 39^3 \) which we already calculated as \( 59319 \):
\[ V_{3.14} = \frac{4}{3} (3.14) (59319) \approx \frac{4}{3} \times 3.14 \times 59319 \]
Calculating this step-by-step:
\[ = \frac{4}{3} \times 186,659.46 \approx 248879.28 \text{ cubic inches} \]
Step 3: Find the difference
Now we find the difference between the two volumes:
\[ \text{Difference} = V_{\pi} - V_{3.14} \approx 248998.293 - 248879.28 \approx 119.013 \text{ cubic inches} \]
Step 4: Round to the nearest tenth
Rounding \( 119.013 \) to the nearest tenth gives:
\[ \text{Difference} \approx 119.0 \text{ cubic inches} \]
Final Result
The difference of using \( \pi \) rather than \( 3.14 \) is about 119.0 cubic inches.