To find the radius [tex]\( r \)[/tex] of a ball given its surface area [tex]\( S \)[/tex], we can use the formula:
[tex]\[ r = \sqrt{\frac{S}{12.6}} \][/tex]
where [tex]\( S \)[/tex] is the surface area in square inches.
Given:
[tex]\[ S = 478.8 \text{ square inches} \][/tex]
We can substitute 478.8 for [tex]\( S \)[/tex] into the formula:
[tex]\[ r = \sqrt{\frac{478.8}{12.6}} \][/tex]
First, we calculate the division inside the square root:
[tex]\[ \frac{478.8}{12.6} \approx 38.0 \][/tex]
Next, we take the square root of the result:
[tex]\[ r = \sqrt{38.0} \approx 6.164414002968976 \][/tex]
Now, we need to round this value to the nearest tenth:
[tex]\[ 6.164414002968976 \approx 6.2 \][/tex]
Therefore, the radius of the ball is approximately [tex]\( 6.2 \)[/tex] inches when rounded to the nearest tenth.
