Please help...

Find the volume of the space inside the right square prism which is not occupied by the two congruent right square pyramids. The height (h) of each square pyramid is 12 cm and the length of the side of the square base is 8 cm.

Question

Please help...

Find the volume of the space inside the right square prism which is not occupied by the two congruent right square pyramids. The height (h) of each square pyramid is 12 cm and the length of the side of the square base is 8 cm.

reds · Answer

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HeartTricker · Answer

Hi, do you know anything about volume?

reds · Answer

@hearttricker yeah I'm just a bit lost in the problem do you know how to help?

HeartTricker · Answer

Yes

the Volume is

$$\frac{ 1 }{3 } a^2h$$

so you do $$\frac{ 1 }{ 3 }x 8 ^2x 12= ?$$

HeartTricker · Answer

? would be your answer :)

AZ · Answer

I disagree with HeartTricker

AZ · Answer

We have a right square prism
And there are two right square pyramids inside

We want to find the volume NOT occupied by the pyramids

That means if we find the total volume of the prism
and we need to subtract the volume of the two pyramids

That would get us the final answer which is the volume of the remaining space in the pyramid

AZ · Answer

Volume of the prism is going to be

Volume = Base * height

Base is the area of the base. Since it's a square base, the area of the base is side^2
and each side is 8 cm
so the area of the base is 8 * 8

and the height of the prism is 12 + 12 = 24

So the volume of the prism is 8 * 8 * 24 = ??

AZ · Answer

The volume of the square pyramid is $\dfrac{1}{3} s^2 h$

the side is 8 and the height of each pyramid is 12

so find the volume of one pyramid and then multiply by 2 because we need the volume of two pyramids

AZ · Answer

To get to your final answer, we need to do

(volume of prism) - (volume of two pyramids) = ??

AZ · Answer

If that's too much for you to understand all at once, I can go over it with you step by step

reds · Answer

I am working on it but I think that would be nice if you would like to go over step by step

reds · Answer

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reds · Answer

am I somewhat on the right track?

ItzAgar · Answer

I don't know the answer, but I hope this could help you at least. https://www.chino.k12.ca.us/cms/lib/CA01902308/Centricity/Domain/4926/12-5_Volumes_of_Pyramids_and_Cones.pdf

AZ · Answer

@reds wrote:

am I somewhat on the right track?

The height of the prism is 24 not 12! If you look in the image, you see that each 'h' is 12 feet and the prism is made up of 2 * h So the volume of the prism is 8 * 8 * 24 = ?? And for the area of the pyramids you forgot to multiply by 1/3 The height of the pyramid is 12 Volume of pyramid = 1/3 * B * h = 1/3 * 64 * 12 and then you multiply by 2 to get the area of 2 pyramids

AZ · Answer

and then you subtract

final answer = (prism volume) minus (2 pyramids volume)

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