To find the radius of a sphere given its surface area, we use the formula for the surface area of a sphere, which is:
[tex]\[ A = 4 \pi r^2 \][/tex]
Where:
- \( A \) is the surface area of the sphere,
- \( r \) is the radius of the sphere,
- \( \pi \) is approximately 3.14159.
Given that the surface area (\( A \)) is 320 square centimeters, we can set up the equation:
[tex]\[ 320 = 4 \pi r^2 \][/tex]
We need to solve for \( r \). First, isolate \( r^2 \) by dividing both sides of the equation by \( 4 \pi \):
[tex]\[ r^2 = \frac{320}{4 \pi} \][/tex]
Next, we calculate the right-hand side of the equation:
[tex]\[ r^2 = \frac{320}{4 \times 3.14159} \][/tex]
[tex]\[ r^2 = \frac{320}{12.56636} \][/tex]
[tex]\[ r^2 \approx 25.452 \][/tex]
Now, take the square root of both sides to find \( r \):
[tex]\[ r \approx \sqrt{25.452} \][/tex]
[tex]\[ r \approx 5.046 \][/tex]
Finally, round the result to 2 decimal places:
[tex]\[ r \approx 5.05 \][/tex]
Thus, the radius of the sphere is approximately 5.05 centimeters.
