Question

The ratio of the volumes of two similar solid polyhedra is equal to the square of the ratio between their edges. True or False?

Answer 1

Answer:

The given statement is false.

Step-by-step explanation:

The ratio of the volumes of two similar solid polyhedra is equal to the square of the ratio between their edges.

This statement is false.

A polyhedron is a shape that has no gaps between their edges or vertices. Like - a cube, prism, or pyramid.

Take in consideration, the cube.

Volume of cubes is given by = $side\times side\times side$ = $side^{3}$

A similar cube will be the one with same dimensions. So, in no way, their volume can be equal to the square of the ratio between their edges.

Answer 2

Answer:

true

Step-by-step explanation:

t is true that; the ratio of the volumes of two similar solid polyhedra is equal to the cube of the ratio between their edges.

Explanation;

The ratio of the corresponding edges or sides or lengths of given similar solids is called the linear scale factor.

The linear scale factor can be used to determine the area scale factor which is the ratio of the area of the similar solids. such that;  Area scale factor is given as the square of the linear scale factor; that is A.S.F = (L.S.F)².

Additionally, the linear scale factor can also be used to find the ratio of the volumes of similar solids, or what is called the volume scale factor; such that the volume scale factor is given by the cube of area scale factor.

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