consider frustum of pyramid w/ sq base w/ side b=7, sq top w

[XBOX999]

Hello, I tried a lot to solve this problem but I have not solved it yet. I want somebody help me solving this problem and tell me the right answer please:

Consider the solid S described below.
A frustum of a pyramid with square base of side b = 7, square top of side a = 5, and height h = 5.
a)Find the volume V of this solid.
V =

b)What happens if a = b? (Enter your answer in terms of b and h.)
we get a ( sphere, tetrahedron, cap of sphere, rectangular solid , square pyramid )
with volume V =

C) What happens if a = 0? (Enter your answer in terms of b and h.)
we get a ( sphere, tetrahedron, cap of sphere, rectangular solid , square pyramid )
with volume V =

 

[Deleted member 4993]

Re: Please Help me as fast as possible

Hello, I tried a lot to solve this problem but I have not solved it yet. I want somebody help me solving this problem and tell me the right answer please:

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you

Consider the solid S described below.
A frustum of a pyramid with square base of side b = 7, square top of side a = 5, and height h = 5.
a)Find the volume V of this solid.
V =

Volume of frustrum = Volume of the Pyramidwithout top cut-off - volume of the cut-off pyramid

To do the above you would have to figure out the heights - using similar (proportional) triangles.

b)What happens if a = b? (Enter your answer in terms of b and h.)
we get a ( sphere, tetrahedron, cap of sphere, rectangular solid , square pyramid )
with volume V =

C) What happens if a = 0? (Enter your answer in terms of b and h.)
we get a ( sphere, tetrahedron, cap of sphere, rectangular solid , square pyramid )
with volume V =

 

[BigGlenntheHeavy]

Re: Please Help me as fast as possible

I'll do A for you and let you go from there. One way:

Volume of a pyramid = (1/3)hB, where h is the height of the pyramid and B is the area of the base.

Let x = extended height of frustrum to obtain a pyramid, then; (5+x)/3.5 = x/2.5, x = 12.5

Hence volume of frustrum = (1/3)(5+12.5)(49) -(1/3)(12.5)(25) = 545/3 = 181.66 cubic units.

 

[deenky]

Why is a Hexagonal Pyramid called a Hexagonal Pyramid? I've googled for a while now and I can't find anything about Hexagonal Pyramids besides nets and how to find the surface area and volume, etc. I need to know for a projects why a hexagonal pyramid is called a hexagonal pyramid. Should I just put because it has a hexagonal base, or is there a better reason?
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