Question

we can use the formula $r = \sqrt{\frac{s}{12.6}}$ to relate a balls surface area $s$ (in square inches) to its radius $r$ (in inches). suppose a ball has a surface area of 415.8 square inches. what is its radius? round your answer to the nearest tenth.

Explanation:

Step1: Identify the given values

We know that the surface area \( S = 415.8 \) square inches and the formula for the radius \( r=\sqrt{\frac{S}{12.6}} \).

Step2: Substitute \( S \) into the formula

Substitute \( S = 415.8 \) into the formula \( r=\sqrt{\frac{S}{12.6}} \), we get \( r=\sqrt{\frac{415.8}{12.6}} \).

Step3: Calculate the fraction inside the square root

First, calculate \( \frac{415.8}{12.6} \). \( \frac{415.8}{12.6}=33 \).

Step4: Take the square root

Now, take the square root of 33. \( \sqrt{33}\approx 5.7446 \).

Step5: Round to the nearest tenth

Rounding \( 5.7446 \) to the nearest tenth gives \( 5.7 \).

Answer:

\( 5.7 \)