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

27 km²

Explanation:

`SA=4\pi Jr^2`

`4\pi r^2_B=432`

`r^2_B=(108)/(\pi)`

`r_B=(6\sqrt3)/(√(50))`

`r_A=(r_B)/(4)=(3\sqrt3)/(2\sqrt\pi)`

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

`=4\pi\bullet(27)/(4\pi)`

`=27\ km`

`Y_B:Y_A=4=1`

`SA_B:SA_A=16:1`

`432/ 16=27\ km^2`

`simple\ relation.`

I hope this helps you

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