Answer: 18.2
Step-by-step explanation: To find the diameter of a sphere given its surface area, you can use the formula:
\[ A = 4 \pi r^2 \]
Where:
- \( A \) is the surface area of the sphere
- \( r \) is the radius of the sphere
First, let's rearrange the formula to solve for the radius, \( r \):
\[ r = \sqrt{\frac{A}{4\pi}} \]
Now, substitute the given surface area \( A = 1041 \) square inches into the formula:
\[ r = \sqrt{\frac{1041}{4\pi}} \]
Let's calculate:
\[ r ≈ \sqrt{\frac{1041}{4 \times 3.14}} \]
\[ r ≈ \sqrt{\frac{1041}{12.56}} \]
\[ r ≈ \sqrt{82.873 }\]
\[ r ≈ 9.098\]
Now, to find the diameter, simply double the radius:
\[ \text{Diameter} = 2 \times r = 2 \times 9.098 ≈ 18.2 \]
So, the diameter of the sphere is approximately 18.2 inches.
