Question

How much larger is the calculation of the volume of a sphere's whose radius is
39 inches if π is used instead of 3.14?



Round your answer to the nearest tenth.



The difference of using π rather than 3.14 is about
cubic inches.

Answer 1

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**.