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 use 3.14 for pi and round answers to the nearest tenth
The formula for the volume of a sphere is: V = (4/3)πг²
The radius of the MSG Sphere is 258 feet
(Put in the length and the unit in the boxes)
The volume of thee MSG Sphere is 71,963,517 cubic feet or ft³
(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 that can fit in the MSG Sphere is *blank* (Round to the nearest whole number)
Make sure no one can find this
Calculate the volume of the MSG Sphere use 3.14 for pi and round answers to the nearest tenth
The formula for the volume of a sphere is: V = (4/3)πг²
The radius of the MSG Sphere is 258 feet
(Put in the length and the unit in the boxes)
The volume of thee MSG Sphere is 71,963,517 cubic feet or ft³
(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 that can fit in the MSG Sphere is *blank* (Round to the nearest whole number)
Make sure no one can find this
Answers
GPT-4o mini
To calculate the volume of the MSG Sphere, we will use the given formula:
\[ V = \frac{4}{3} \pi r^3 \]
First, we need to find the radius. According to your information, the radius is 258 feet. Now, we will plug in the values into the formula with \( \pi \approx 3.14 \):
1. Calculate \( r^3 \):
\[
r^3 = 258^3 = 17,202,432
\]
2. Now apply the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 17,202,432
\]
3. Calculate \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.18667
\]
4. Finally, calculate the volume:
\[
V \approx 4.18667 \times 17,202,432 \approx 71,930,000
\]
Rounding this to the nearest whole number gives us:
\[
V \approx 71,930,000 \text{ cubic feet}
\]
So the volume of the MSG Sphere is **71,930,000 ft³**.
#### Calculating the number of Olympic swimming pools:
Given that one Olympic swimming pool holds about \( 124,000 \) cubic feet of water, we can divide the volume of the Sphere by the volume of one Olympic swimming pool:
\[
\text{Number of pools} = \frac{71,930,000}{124,000} \approx 580.65
\]
Rounding this to the nearest whole number gives:
\[
\text{Number of pools} \approx 581
\]
Therefore, the number of Olympic swimming pools that can fit in the MSG Sphere is **581**.
\[ V = \frac{4}{3} \pi r^3 \]
First, we need to find the radius. According to your information, the radius is 258 feet. Now, we will plug in the values into the formula with \( \pi \approx 3.14 \):
1. Calculate \( r^3 \):
\[
r^3 = 258^3 = 17,202,432
\]
2. Now apply the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 17,202,432
\]
3. Calculate \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.18667
\]
4. Finally, calculate the volume:
\[
V \approx 4.18667 \times 17,202,432 \approx 71,930,000
\]
Rounding this to the nearest whole number gives us:
\[
V \approx 71,930,000 \text{ cubic feet}
\]
So the volume of the MSG Sphere is **71,930,000 ft³**.
#### Calculating the number of Olympic swimming pools:
Given that one Olympic swimming pool holds about \( 124,000 \) cubic feet of water, we can divide the volume of the Sphere by the volume of one Olympic swimming pool:
\[
\text{Number of pools} = \frac{71,930,000}{124,000} \approx 580.65
\]
Rounding this to the nearest whole number gives:
\[
\text{Number of pools} \approx 581
\]
Therefore, the number of Olympic swimming pools that can fit in the MSG Sphere is **581**.