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Gwar [14]
2 years ago
7

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.

Mathematics
1 answer:
Sergeeva-Olga [200]2 years ago
7 0
<h2>Answer:</h2>

27 km²

<h2>Step-by-step explanation:</h2>

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.

<em>I hope this helps you</em>

<em>:)</em>

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