Dexter bought a glass pyramid from a gift store. The pyramid, with a height of 5 cm and a square base of side 3 cm, was packed in a box shaped as a cube of side 6 cm. The empty space in the box was packed with paper tissue.

How many cubic centimeters of the box were stuffed with paper tissue?

Question

Dexter bought a glass pyramid from a gift store. The pyramid, with a height of 5 cm and a square base of side 3 cm, was packed in a box shaped as a cube of side 6 cm. The empty space in the box was packed with paper tissue. 
 
How many cubic centimeters of the box were stuffed with paper tissue?

istim · Answer

Isn't it just the volume of the cube subtracted by the volume of the pyramid then?

istim · Answer

In such case the formula for the cube's volume is v=lwh, but I don't know what the formula would be for the square-based pyramid.

anonymous · Answer

I am not really sure.. but i think the answer is 201... ? Is that correct?

istim · Answer

I don't know. Haven't done the math myself.

anonymous · Answer

can you do it? lol

istim · Answer

I'm a bit busy myself. Have confidence. Try re-doing it without looking at your original work if you truly are concerned.

istim · Answer

Oh, volume for square-based pyramid is v=1/3b^2h

istim · Answer

I'm trying to help.

anonymous · Answer

I know. thanks.. ill try with the formula u gave me..

istim · Answer

So I guess your complete formula for the paper tissue is v=lwh -1/3b^2h

anonymous · Answer

ahh i don't have the length though.

istim · Answer

Which one?

istim · Answer

The cube? All lengths are the same. It's like s^3.

anonymous · Answer

of the pyramid.... i need lwh don't i?

istim · Answer

LWh is the cube...

anonymous · Answer

ohh. so its all the same??

istim · Answer

What's the same?

istim · Answer

Are you good then?

anonymous · Answer

im so confused to be honest..

istim · Answer

Hello?

istim · Answer

What's the confusion? Just read their our chat to understand...

anonymous · Answer

what??

istim · Answer

I don't see what the confusion is.

anonymous · Answer

how to get the answer. if you don't understand what the confusion is.. can you help me, and give me an answer! pleassseee.

istim · Answer

I gave you the combined formula, v=lwh -1/3b^2h. Just plug and play.

anonymous · Answer

i did. but i don't have all the things needed for the equation!!!

istim · Answer

The values themselves are given in your question.

anonymous · Answer

not all of them..

istim · Answer

lwh is the cube. The other one is the square-based pyramid.

anonymous · Answer

can you help me plug them in ? please

istim · Answer

l,w and h are all 6.

anonymous · Answer

okay. so v=lwh -1/3b^2h, v=(6)(6)(6)- 1/3(5^2)(3)

istim · Answer

Because it is a cube. Cubes have side lengths which are all the same.

anonymous · Answer

are you sure the pyramid formula is squared?

istim · Answer

It's not squared. Ignore that if you don't understand.

anonymous · Answer

ohh. okay. so then its just  v=(6)(6)(6)- 1/3(5)(3), 216-5=209?

anonymous · Answer

i mean.. 211?

istim · Answer

I don't know actually. I haven't done the calculations myself.

anonymous · Answer

Woah. I'm sorry. thanks you really helped! I got the question CORRECT:) anddd can you help me with my other questions.

anonymous · Answer

Ross is constructing two similar boxes shaped as similar rectangular prisms. The larger box has a height of 20 inches and a square base of side length 12 inches. 
 
If the smaller box has a height of 15 inches, what is its volume?

istim · Answer

Uh. Maybe ask the other guys.

anonymous · Answer

lol. kk