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The circumference of the Spaceship Earth at Epcot Center is 518.1 feet. Determine Spaceship Earth's approximate volume.(5 points)
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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 areaand the unit we would use is Response area.

1 answer

To determine the approximate volume of Spaceship Earth using its circumference, we will follow these steps.

Step 1: Find the radius using the formula for circumference

Given:

  • Circumference (C) = 518.1 feet

The formula for circumference is: \[ C = 2\pi r \]

We can rearrange this to solve for the radius (r): \[ r = \frac{C}{2\pi} \]

Substituting the given value: \[ r = \frac{518.1}{2\pi} \] \[ r \approx \frac{518.1}{6.2832} \] \[ r \approx 82.6 \text{ feet} \]

Step 2: Calculate the volume using the formula for the volume of a sphere

The volume (V) of a sphere is given by the formula: \[ V = \frac{4}{3}\pi r^3 \]

Now we will substitute the radius we calculated: \[ V = \frac{4}{3}\pi (82.6)^3 \]

Calculating \( (82.6)^3 \): \[ (82.6)^3 \approx 564,845.2 \]

Now substituting this into the volume formula: \[ V \approx \frac{4}{3} \cdot \pi \cdot 564,845.2 \] \[ V \approx \frac{4}{3} \cdot 3.1416 \cdot 564,845.2 \] \[ V \approx \frac{4 \cdot 3.1416 \cdot 564,845.2}{3} \] \[ V \approx \frac{7,086,601.6}{3} \] \[ V \approx 2,362,200.5 \text{ cubic feet} \]

Final Response

The approximate volume of Spaceship Earth is 2,362,200.5 cubic feet.

  1. Step 1 Response: Define the radius (r) = 82.6 feet.
  2. Step 2 Response: Calculate the sphere volume = 2,362,200.5 cubic feet.
  3. Final Answer Response: The answer is approximately 2,362,200.5 and the unit we would use is cubic feet.