To determine the volume of water that a large reservoir, modeled as a hemisphere, can hold when its radius is 630 meters, we start with the given volume formula for a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3, \][/tex]
where [tex]\( r \)[/tex] is the radius.
### Step 1: Calculate the volume of a full sphere
We substitute [tex]\( r = 630 \)[/tex] meters into the formula:
[tex]\[ V_{\text{sphere}} = \frac{4}{3} \pi (630)^3. \][/tex]
### Step 2: Simplify the expression
First, compute the value of [tex]\( (630)^3 \)[/tex]:
[tex]\[ 630^3 = 250047000. \][/tex]
Next, multiply this result by [tex]\( \frac{4}{3} \)[/tex] and [tex]\( \pi \)[/tex]:
[tex]\[ V_{\text{sphere}} = \frac{4}{3} \pi \times 250047000. \][/tex]
Using the value [tex]\( \pi \approx 3.141592653589793 \)[/tex], we get:
[tex]\[ V_{\text{sphere}} = \frac{4}{3} \times 3.141592653589793 \times 250047000 \approx 1047394424.34 \ \text{cubic meters}. \][/tex]
### Step 3: Calculate the volume of the hemisphere
Since the reservoir is modeled as a hemisphere (half of a sphere), we need to divide the volume of the sphere by 2:
[tex]\[ V_{\text{hemisphere}} = \frac{V_{\text{sphere}}}{2} \approx \frac{1047394424.34}{2} = 523697212.17 \ \text{cubic meters}. \][/tex]
### Step 4: Express the volume in scientific notation
To express [tex]\( V_{\text{hemisphere}} \)[/tex] in scientific notation, with two decimal places, we write:
[tex]\[ 523697212.17 \approx 5.24 \times 10^8 \ \text{cubic meters}. \][/tex]
### Conclusion
Therefore, the volume of water the reservoir can hold is approximately:
[tex]\[ \boxed{5.24 \times 10^8 \ \text{cubic meters}}. \][/tex]
This completes our calculation for the application problem, providing the volume of the hemisphere-shaped reservoir in scientific notation with two decimal places of accuracy.
