Question
The Las Vegas sphere, officially known as the MSG sphere, is a state of the art entertainment venue that opened in 2023. Located near the Venetian resort, it stands 366 feet tall with a diameter of 516 feet, making it the world's largest spherical structure. The exterior is covered in 1.2 million LED pucks, creating a dynamic, immersive display. Inside, it features a 160,000 square foot 16k resolution wraparound screen and a 164,000 speaker audio system. Construction began in 2018, costing approximately $2.3 billion. The sphere is designed to revolutionize live entertainment, offering unique sensory experiences through advanced sound and visual technologies.
Calculate the volume of the MSG sphere on a peice of paper then transfer your answer below. Use 3.14 for pi and round answers to the nearest tenth.
The formula for the volume of a sphere is____
The radius of the MSG sphere _____ _____ (put in the length and the unit in the boxes)
The volume of the MSG sphere is _____ cubic feet or ft^3 (type in the volume using commas to separate periods and round to the nearest whole number)
If one olympic swimming pool holds about 124,000 cubic feet of water, the number of Olympic swimming pools can fit in the MSG sphere is ______ (round to the nearest whole number)
Calculate the volume of the MSG sphere on a peice of paper then transfer your answer below. Use 3.14 for pi and round answers to the nearest tenth.
The formula for the volume of a sphere is____
The radius of the MSG sphere _____ _____ (put in the length and the unit in the boxes)
The volume of the MSG sphere is _____ cubic feet or ft^3 (type in the volume using commas to separate periods and round to the nearest whole number)
If one olympic swimming pool holds about 124,000 cubic feet of water, the number of Olympic swimming pools can fit in the MSG sphere is ______ (round to the nearest whole number)
Answers
GPT-4o mini
Let's go through the calculations step by step.
1. **The formula for the volume of a sphere is**:
\[ V = \frac{4}{3} \pi r^3 \]
2. **The radius of the MSG sphere**:
The diameter of the MSG sphere is 516 feet, so the radius (r) is half of that:
\[ r = \frac{516}{2} = 258 \text{ feet} \]
3. **The volume of the MSG sphere**:
Using the formula \( V = \frac{4}{3} \pi r^3 \) with \( r = 258 \) feet and \( \pi \approx 3.14 \):
\[
V = \frac{4}{3} \times 3.14 \times (258)^3
\]
First, calculate \( 258^3 \):
\[
258^3 = 258 \times 258 \times 258 = 17,188,032
\]
Now plug this value back into the formula:
\[
V = \frac{4}{3} \times 3.14 \times 17,188,032
\]
\[
V \approx \frac{4}{3} \times 3.14 \times 17,188,032 \approx \frac{4 \times 3.14 \times 17,188,032}{3}
\]
\[
V \approx \frac{215,195,941.76}{3} \approx 71,731,980.6 \text{ cubic feet}
\]
Rounding to the nearest whole number:
\[ V \approx 71,731,981 \text{ cubic feet or ft}^3 \]
4. **The number of Olympic swimming pools that can fit in the MSG sphere**:
An Olympic swimming pool holds about 124,000 cubic feet of water.
\[ \text{Number of pools} = \frac{71,731,981}{124,000} \approx 578.3 \]
Rounding to the nearest whole number, we get:
\[ \text{Number of Olympic swimming pools} \approx 578 \]
Now, let's summarize the findings:
- **The formula for the volume of a sphere is**: \( V = \frac{4}{3} \pi r^3 \)
- **The radius of the MSG sphere is**: 258 feet
- **The volume of the MSG sphere is**: 71,731,981 cubic feet or ft^3
- **The number of Olympic swimming pools that can fit in the MSG sphere is**: 578
1. **The formula for the volume of a sphere is**:
\[ V = \frac{4}{3} \pi r^3 \]
2. **The radius of the MSG sphere**:
The diameter of the MSG sphere is 516 feet, so the radius (r) is half of that:
\[ r = \frac{516}{2} = 258 \text{ feet} \]
3. **The volume of the MSG sphere**:
Using the formula \( V = \frac{4}{3} \pi r^3 \) with \( r = 258 \) feet and \( \pi \approx 3.14 \):
\[
V = \frac{4}{3} \times 3.14 \times (258)^3
\]
First, calculate \( 258^3 \):
\[
258^3 = 258 \times 258 \times 258 = 17,188,032
\]
Now plug this value back into the formula:
\[
V = \frac{4}{3} \times 3.14 \times 17,188,032
\]
\[
V \approx \frac{4}{3} \times 3.14 \times 17,188,032 \approx \frac{4 \times 3.14 \times 17,188,032}{3}
\]
\[
V \approx \frac{215,195,941.76}{3} \approx 71,731,980.6 \text{ cubic feet}
\]
Rounding to the nearest whole number:
\[ V \approx 71,731,981 \text{ cubic feet or ft}^3 \]
4. **The number of Olympic swimming pools that can fit in the MSG sphere**:
An Olympic swimming pool holds about 124,000 cubic feet of water.
\[ \text{Number of pools} = \frac{71,731,981}{124,000} \approx 578.3 \]
Rounding to the nearest whole number, we get:
\[ \text{Number of Olympic swimming pools} \approx 578 \]
Now, let's summarize the findings:
- **The formula for the volume of a sphere is**: \( V = \frac{4}{3} \pi r^3 \)
- **The radius of the MSG sphere is**: 258 feet
- **The volume of the MSG sphere is**: 71,731,981 cubic feet or ft^3
- **The number of Olympic swimming pools that can fit in the MSG sphere is**: 578