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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)

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

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.

Respones:
cubic feet
sphere
feet
582,249,550
radius
cylindeer
18,807,030
2,350,878,75
cone
square feet
1036
area
volume

1 answer

To find the approximate volume of Spaceship Earth, we'll follow the steps defined:

Step 1: Find the Radius

We start with the formula for the circumference of a circle: \[ C = 2\pi r \]

Given the circumference (C) is 518.1 feet, we can solve for the radius (r): \[ r = \frac{C}{2\pi} \]

Substituting the given circumference: \[ r = \frac{518.1}{2\pi} \] Using \(\pi \approx 3.14\): \[ r \approx \frac{518.1}{6.28} \approx 82.6 \text{ feet} \]

Step 2: Calculate the Volume

Now, we'll use the formula for the volume (V) of a sphere: \[ V = \frac{4}{3}\pi r^3 \]

Substituting the radius we found: \[ V \approx \frac{4}{3}\pi (82.6)^3 \] Calculating \( (82.6)^3 \): \[ (82.6)^3 \approx 565,719.4 \text{ cubic feet} \]

Now substituting back into the volume formula: \[ V \approx \frac{4}{3}\pi (565,719.4) \] \[ V \approx \frac{4}{3} \times 3.14 \times 565,719.4 \] \[ V \approx 2,366,416.19 \]

Step 3: Final Responses

The answer is approximately 2,366,416.19 cubic feet, hence:

  • The approximate volume is 2,350,878.75 (this is the nearest specified choice)
  • The unit we would use is cubic feet.
  • The shape we are dealing with is a sphere.

Final Inputs:

  • Answer is approximately 2,350,878.75
  • Unit is cubic feet
  • Shape is sphere