Given:
The surface area of a soap bubble varies directly as the square of the radius of the bubble.
Let the surface area = A
Let the radius = r
so,
[tex]\begin{gathered} A\propto r^2 \\ A=k\cdot r^2 \end{gathered}[/tex]where: (k) is the constant of proportionality
If a bubble with a radius of 3 inches has a surface area of 113 square inches
so,
When r = 3 inches, A = 113 square inches
Substitute with (r) and (A) to find the value of (k)
[tex]\begin{gathered} 113=k\cdot3^2 \\ 113=9k \\ k=\frac{113}{9} \end{gathered}[/tex]so, the equation will be:
[tex]A=(\frac{113}{9})r^2[/tex]we will find the surface area when the radius = 4 inches
So, when r = 4 inches
[tex]A=(\frac{113}{9})\cdot4^2=\frac{113}{9}\cdot16=200.8889[/tex]Rounding to the nearest tenth
So, the answer will be: the surface area = 200.9 square inches
