Question

The circumference of the Spaceship Earth at Epcot Center is 518.1 feet. Determine Spaceship Earth's approximate volume.(5 points)
Step 1: You will need to find the (Response area) using the formula: C = 2πr

Step 2: You will need to substitute your answer into the (Response area) formula for a (Response area.)

Step 3: The answer is approximately (Response area) and the unit we would use is (Response area.)

options for the response areas: radius, 2,350,878.75, square feet, sphere, volume, cone, cylinder, area, 582,249,550, 1036, feet, cubic feet, 18,807,030

Answer 1

To determine the approximate volume of Spaceship Earth using its circumference, we can follow the steps outlined:

### Step 1: Find the radius
The formula for circumference (C) of a sphere is given by:

\[
C = 2\pi r
\]

We can rearrange this formula to solve for the radius (r):

\[
r = \frac{C}{2\pi}
\]

Now, substitute the given circumference:

\[
r = \frac{518.1}{2\pi} \approx \frac{518.1}{6.2832} \approx 82.6 \text{ feet}
\]

### Step 2: Substitute into the volume formula
The volume (V) of a sphere is given by:

\[
V = \frac{4}{3}\pi r^3
\]

Now we can substitute our calculated radius (r):

\[
V \approx \frac{4}{3}\pi (82.6)^3
\]

Calculating \( (82.6)^3 \):

\[
(82.6)^3 \approx 565,704.976
\]

Then plugging that back into the volume formula:

\[
V \approx \frac{4}{3} \pi (565,704.976) \approx \frac{4}{3} \cdot 3.1416 \cdot 565,704.976
\]

This results in:

\[
V \approx \frac{4}{3} \cdot 3.1416 \cdot 565,704.976 \approx 2,373,867.3 \text{ cubic feet}
\]

### Step 3: Provide the final answer
The approximate answer is:

The volume of Spaceship Earth is approximately **2,373,867.3** cubic feet.

Given your options, let's fill in the response areas:

1. **radius**
2. **2,373,867.3**
3. **cubic feet**

So, the response areas are:

1. radius
2. 2,373,867.3
3. cubic feet