The effect this scale factor has on the volume is that the volume will be 64 times larger. The correct option is B.
What is a Scale factor?
Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. They have scaled versions of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.
So, if a side of a 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 a scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple linear things twice grow by the square of the scale factor. Thus, we need to multiply or divide by k².
to get each other corresponding quantities from their similar figures' quantities.
So the area of the first figure = k² × area of the second figure
Similarly, increasing product-derived quantities will need increased power of 'k' to get the corresponding quantity. Thus, for volume, it is k cubed. or
The volume of the first figure = k³ × volume of the 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.
Since the volume is the product of three linear quantities.
Therefore, if the scale factor of 4 is applied to the given prism then the volume of the prism will grow by 4³. Thus, we can write,
The volume of the scaled prism = 4³ ×Volume of the original volume
The volume of the scaled prism = 64 ×Volume of the original volume
Hence, the effect this scale factor has on the volume is that the volume will be 64 times larger.
Learn more about Scale factors here:
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