Question
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.
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.
Answers
GPT-4o mini
To find the approximate volume of Spaceship Earth, we'll go through the steps you've outlined:
### Step 1: Find the radius (r) using the circumference formula
The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
Given that the circumference C = 518.1 feet, we can rearrange the formula to solve for the radius (r):
\[ r = \frac{C}{2\pi} \]
Substituting the given circumference:
\[ r = \frac{518.1}{2\pi} \]
Calculating the radius:
\[ r \approx \frac{518.1}{6.2832} \approx 82.5 \text{ feet} \]
### Step 2: Use the radius to find the volume (V)
The formula for the volume (V) of a sphere is:
\[ V = \frac{4}{3}\pi r^3 \]
Substituting the value of r we calculated:
\[ V \approx \frac{4}{3}\pi (82.5)^3 \]
Calculating \( (82.5)^3 \):
\[ (82.5)^3 \approx 561,900.625 \]
Now substituting into the volume formula:
\[ V \approx \frac{4}{3}\pi (561,900.625) \]
\[ V \approx \frac{4}{3} \times 3.1416 \times 561,900.625 \approx 2,358,284.882 \]
### Step 3: Rounding the answer
The answer is approximately:
\[ V \approx 2,358,285 \text{ cubic feet (ft}^3\text{)} \]
### Responses for Input
1. Response area: 2,358,285
2. Unit for Response area: cubic feet (ft³)
So you would fill in your responses as:
- Response area: 2,358,285
- Unit: cubic feet (ft³)
### Step 1: Find the radius (r) using the circumference formula
The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
Given that the circumference C = 518.1 feet, we can rearrange the formula to solve for the radius (r):
\[ r = \frac{C}{2\pi} \]
Substituting the given circumference:
\[ r = \frac{518.1}{2\pi} \]
Calculating the radius:
\[ r \approx \frac{518.1}{6.2832} \approx 82.5 \text{ feet} \]
### Step 2: Use the radius to find the volume (V)
The formula for the volume (V) of a sphere is:
\[ V = \frac{4}{3}\pi r^3 \]
Substituting the value of r we calculated:
\[ V \approx \frac{4}{3}\pi (82.5)^3 \]
Calculating \( (82.5)^3 \):
\[ (82.5)^3 \approx 561,900.625 \]
Now substituting into the volume formula:
\[ V \approx \frac{4}{3}\pi (561,900.625) \]
\[ V \approx \frac{4}{3} \times 3.1416 \times 561,900.625 \approx 2,358,284.882 \]
### Step 3: Rounding the answer
The answer is approximately:
\[ V \approx 2,358,285 \text{ cubic feet (ft}^3\text{)} \]
### Responses for Input
1. Response area: 2,358,285
2. Unit for Response area: cubic feet (ft³)
So you would fill in your responses as:
- Response area: 2,358,285
- Unit: cubic feet (ft³)