To find the volume of a hemisphere with a given radius, you can use the formula for the volume of a hemisphere. The formula for the volume [tex]\( V \)[/tex] of a hemisphere is:
[tex]\[ V = \frac{2}{3} \pi r^3 \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the hemisphere
- [tex]\( \pi \)[/tex] (pi) is a mathematical constant approximately equal to 3.14159
Given:
- The radius [tex]\( r \)[/tex] of the hemisphere is 8 centimeters
Let's plug the given radius into the formula:
1. First, compute [tex]\( r^3 \)[/tex]:
[tex]\[ r^3 = 8^3 = 512 \][/tex]
2. Then multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[ \pi \times 512 \approx 3.14159 \times 512 \approx 1609.438 \][/tex]
3. Now, multiply this result by [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[ \frac{2}{3} \times 1609.438 \approx 1072.330 \][/tex]
So, the volume of the hemisphere is:
[tex]\[ 1072.330 \, \text{cm}^3 \][/tex]
4. Finally, round this value to the nearest whole number:
[tex]\[ 1072.330 \approx 1072 \][/tex]
Thus, the volume of the hemisphere with a radius of 8 centimeters is approximately [tex]\( 1072 \, \text{cm}^3 \)[/tex] when rounded to the nearest whole number.
