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Sphere B is the image of sphere A after dilation by a scale factor of 44. If the surface area of sphere B is 432 km^2, find the surface area of sphere A, the preimage.

Sphere B is the image of sphere A after dilation by a scale factor of 44 If the surface area of sphere B is 432 km2 find the surface area of sphere A the preima class=

Respuesta :

Answer:

27 km²

Step-by-step explanation:

[tex]SA=4\pi Jr^2[/tex]

  [tex]4\pi r^2_B=432[/tex]

      [tex]r^2_B=\frac{108}{\pi}[/tex]

      [tex]r_B=\frac{6\sqrt3}{\sqrt{50}}[/tex]

[tex]r_A=\frac{r_B}{4}=\frac{3\sqrt3}{2\sqrt\pi}[/tex]

[tex]S_0SA=4\pi Y\begin{matrix}2\\A\\\end{matrix}[/tex]

         [tex]=4\pi\bullet\frac{27}{4\pi}[/tex]

         [tex]=27\ km[/tex]

   [tex]Y_B:Y_A=4=1[/tex]

  [tex]SA_B:SA_A=16:1[/tex]

                 [tex]432\div 16=27\ km^2[/tex]

                          [tex]simple\ relation.[/tex]

I hope this helps you

:)