Question

we can use the formula $r = sqrt{\frac{s}{12.6}}$ to relate a balls surface area $s$ (in square centimeters) to its radius $r$ (in centimeters). suppose a ball has a radius of 13.79 centimeters. what is its surface area? carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.

Explanation:

Step1: Square both sides of the formula

Given $r = \sqrt{\frac{S}{12.6}}$, squaring both sides gives $r^{2}=\frac{S}{12.6}$.

Step2: Solve for S

Multiply both sides of the equation $r^{2}=\frac{S}{12.6}$ by 12.6. So $S = 12.6r^{2}$.

Step3: Substitute the value of r

Substitute $r = 13.79$ into the formula $S = 12.6r^{2}$. Then $S=12.6\times(13.79)^{2}$.
First, calculate $(13.79)^{2}=190.1641$.
Then, $S = 12.6\times190.1641=2396.06766$.

Step4: Round the answer

Round $2396.06766$ to the nearest tenth. The result is $2396.1$.

Answer:

$2396.1$