The volume of one prism = [tex] 1458 mm^3 [/tex]
The volume of other prism = [tex] 16 mm^3 [/tex]
The first prism is scaled down to the second prism. As volume given, to find the scale factor we will have to find cube root of the ratio of the volume. So the scale factor is
[tex] (\frac{16}{1458})^{(1/3)} [/tex]
We have to simplify the fraction now. To simplify it we will divide the numerator and denominator by a common factor of them.
2 is a common factor of 1458 and 16. By dividing them by 2 we will get,
[tex] \frac{16}{1458} = \frac{8}{729} [/tex]
Now we have to find cube root of both 8 and 729.
We know that, [tex] 2^3 =8 [/tex]. So cube root of 8 is 2.
And also, [tex] 9^3 = 729 [/tex]. So cube root of 729 is 9.
The scale factor is = [tex] \frac{2}{9} [/tex].
We have got the required answer. Option A is the correct option here.
