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

Mathematics

2 answers:

Svetllana [295]3 years ago

5 0

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.

ad-work [718]3 years ago

3 0

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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3 years ago

A cylindrical milk storage tank needs to be built to hold 84.78 cubic feet of milk. The foundation for the tank has already been

Romashka [77]

Answer:

3 or 2.999 (probably 3)

Step-by-step explanation:

So the volume of a cylinder = πr^2 * h

h = height

r = radius

now we know the radius. Leaving us with a simple equation which is:

π*9*h = 9π*h = 84.78 =

π*h = 9.42

h = 9.42 / π = 2.99847912785......

but we can round this to 2.999 or just 3. if you use 2.999 the volume is 84.79 which is as close as I'm gonna try to get. And you might ask why we're rounding to 2.999 and not 2.998? This is because that huge number is the minimum. And 2.998 is smaller than that huge number, meaning it would technically be less than 84.78 cubic ft. But this doesn't really matter because the answer your teacher is probably looking for is 3.

Reference my work if you're are confused, however, it's really messy so sorry about that.