Respuesta :
The quantities which are squares or multiple of linear things twice grow by square of scale factor. The volume of rectangular prism A = 64 m³
How does dilation affect length, area, and volume of an object?
Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.
So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:
L = k × M
where 'k' will be called as scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.
So, area of first figure = k² × area of second figure
Similarly, Volume of first figure = k³ × volume of second figure.
It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.
Given that the Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of 1/2.
Scale factor = (Length of rectangular prism B)/(Length of rectangular prism A)
1/2 = (Length of rectangular prism B)/(Length of rectangular prism A)
Now, the volume of the rectangular prism can be written as,
(Scale factor)³ = (Volume of rectangular prism B)/(Volume of rectangular prism A)
(1/2)³ = 8 m³ /(Volume of rectangular prism A)
The volume of rectangular prism A = 64 m³
Hence, The volume of rectangular prism A = 64 m³
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