The volume of a cube is 48 cubic feet. What is the volume of a pyramid that fits exactly inside the cube? Provide an explanation and proof for your answer to receive full credit.

Question

anonymous · Answer

The volume of the cone is 1/3 the volume of the cube. I divide 48 by 3 and i get 16.  
The volume of a pyramid is 1/3 Bh, where B is the area of the base and h is the height. The volume of a cube is a^3 where a is the side of the cube.
If a pyramid fits in a cube with side "a", then the base is a square, with sides a by a, and the height is also a.When you find the volume of this pyramid using the formula, you get: 
V = 1/3 Bh = 1/3 (a * a) * a  = 1/3 a^3, which is 1/3 the volume of the cube which was a^3.

anonymous · Answer

@is3535 this is what i got but idk if i right at all im not very good at these questions

anonymous · Answer

That's correct

anonymous · Answer

@M4thM1nd thank you! can u help me with another

anonymous · Answer

Sure!

anonymous · Answer

Pyramid A is a square pyramid with a base side length of 18 inches and a height of 9 inches. Pyramid B has a volume of 3136 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percent. Provide an explanation and proof for your answer to receive full credit.

anonymous · Answer

Ok, we know the equation for the pyramid volume, which is: $$V = \frac{1}{3}A_{base}h$$

anonymous · Answer

What is the $A_{base}$ of pyramid A?

xapproachesinfinity · Answer

your answer is good $$V_{pyramid}=\frac{1}{3}a^3=\frac{1}{3}V_{cube}$$

xapproachesinfinity · Answer

you reasoning is just perfect :)

anonymous · Answer

thank you! @xapproachesinfinity  one sec @M4thM1nd  im going to try this on my own then ppst what i got is that okay??

anonymous · Answer

Okay ^^

anonymous · Answer

umm so this is what i got so far I got the volume of Pyramid A:

Pyramid A's volume is 972
because V = Base side length^2 x h/3
V = 18^2 x 9/3 = 972.

anonymous · Answer

That's right!

anonymous · Answer

okay so then do i divide the smaller number by the larger number then multiply that by 100 and round if needed

anonymous · Answer

Now, we know the volume of pyramid B, 3136 in^3, what is the percentage difference?

anonymous · Answer

then i get 972/3136 = 0.30994898 x 100 = 30.99. So would it be 31% or 30%?

anonymous · Answer

that's it xD

anonymous · Answer

31%

anonymous · Answer

thank you sooo much!!! i have a few more let me finish typing out this questions answer in my quize then ill post another if you can still help me?!?!

anonymous · Answer

No problem ^^