Question

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.

Answer 1

Answer:

27 km²

Step-by-step explanation:

$SA=4\pi Jr^2$

  $4\pi r^2_B=432$

      $r^2_B=\frac{108}{\pi}$

      $r_B=\frac{6\sqrt3}{\sqrt{50}}$

$r_A=\frac{r_B}{4}=\frac{3\sqrt3}{2\sqrt\pi}$

$S_0SA=4\pi Y\begin{matrix}2\\A\\\end{matrix}$

         $=4\pi\bullet\frac{27}{4\pi}$

         $=27\ km$

   $Y_B:Y_A=4=1$

  $SA_B:SA_A=16:1$

                 $432\div 16=27\ km^2$

                          $simple\ relation.$

I hope this helps you

:)