2. you have a set of three similar gift boxes. each box is a rectangular prism. the large box has 15-cm base edges. the medium box has 10-cm base edges. the small box has 5-cm base edges. how does the volume of each box compare to every other box?

The volume of the medium box is 8 times the volume of the small box

The volume of the large box is 3.375 times the volume of the medium box

The volume of the large box is 27 times the volume of the small box

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

In this problem

1) The scale factor of the small box to the medium box  is equal to

The scale factor elevated to the cube is equal to

therefore

The volume of the medium box is 8 times the volume of the small box

2) The scale factor of the medium box to the large box  is equal to

The scale factor elevated to the cube is equal to

therefore

The volume of the large box is 3.375 times the volume of the medium box

3) The scale factor of the small box to the large box  is equal to

The scale factor elevated to the cube is equal to

therefore

The volume of the large box is 27 times the volume of the small box

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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