What is dilation?
Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor.
The new figure obtained after dilation is called image.
Scale factor is the ratio of the sizes of the original figure with the dilated figure.
[tex]scale factor = \frac{dimension of new shape }{dimension of original shape}[/tex]
According to the given question
Volume of solid = 6 cubic units
Surface area of solid = 22 square units
volume of image = 48 cubic units
therefore,
ratio of volumes = ratio of lengths
[tex]\frac{48}{6}[/tex] [tex]=8:1[/tex]
⇒ratio of sides = [tex]\sqrt[3]{8} :\sqrt[3]{1}[/tex]
⇒ ratio of sides = 2 : 1
Ratio of surface area of solid and image = square of ratio of sides = 4:1
⇒[tex]\frac{surface area of image }{surface area of solid} = \frac{4}{1}[/tex]
⇒[tex]\frac{surface area of image }{22} = \frac{4}{1}[/tex]
⇒ surface area of image = 4×21
⇒ surface area of image = 81square units.
Learn more about the surface area of dilated things here:
https://brainly.in/question/100815
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