Question

Using the volume of the sphere: V =(4/3)πr³
If the RADIUS of the MSG square is 258 feet,
The volume of thee MSG Sphere is ______ cubic feet.
Type 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 ______ Round to the nearest whole number

Answer 1

To find the volume of the MSG Sphere using the formula for the volume of a sphere \( V = \frac{4}{3} \pi r^3 \), we first need to plug in the radius.

Given that the radius \( r \) is 258 feet:

\[
V = \frac{4}{3} \pi (258)^3
\]

Calculating \( (258)^3 \):

\[
(258)^3 = 17,196,192
\]

Now plug this value into the volume formula:

\[
V = \frac{4}{3} \pi (17,196,192)
\]

Using \( \pi \approx 3.14159 \):

\[
V \approx \frac{4}{3} \times 3.14159 \times 17,196,192
\]

Calculating \( \frac{4}{3} \times 3.14159 \approx 4.18879 \):

\[
V \approx 4.18879 \times 17,196,192 \approx 71,230,230.69
\]

Rounding to the nearest whole number, the volume of the MSG Sphere is:

\[
V \approx 71,230,231 \text{ cubic feet}
\]

Now, to find how many Olympic swimming pools fit in the MSG Sphere, we divide the volume of the sphere by the volume of one Olympic swimming pool:

\[
\text{Number of pools} = \frac{71,230,231}{124,000}
\]

Calculating this:

\[
\text{Number of pools} \approx 574.39
\]

Rounding to the nearest whole number, the number of Olympic swimming pools that can fit in the MSG Sphere is:

\[
\text{Number of pools} \approx 574
\]

In summary:
- The volume of the MSG Sphere is **71,230,231 cubic feet**.
- The number of Olympic swimming pools that can fit in the MSG Sphere is **574**.