We are given area of the spherical lampshade = 57.76 \pi square inches.
We know formula of area of a spherical shape:
[tex]A = 4\pi r^2[/tex]
Plugging area A= 57.76 π in formula, we get
[tex]57.76\pi= 4\pi r^2[/tex]
Dividing both sides by 4π, we get
[tex]\frac{57.76\pi}{4\pi} = \frac{4\pi r^2}{4\pi}[/tex]
[tex]14.44 = r^2[/tex]
Taking square root on both sides, we get
[tex]\sqrt{14.44} = \sqrt{r^2}[/tex]
r =3.8.
