Pyramid A is a square pyramid with a base side length of 14 inches and a height of 6 inches. Pyramid B has a volume of 3,136 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.

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Pyramid A is a square pyramid with a base side length of 14 inches and a height of 6 inches. Pyramid B has a volume of 3,136 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.

Mathematics
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first step: find the area of the base of pyramid A if the base of pyramid A is a square with sides 14, what is the area of the square?
yes
how can i find the area

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Other answers:

area = (side length)^2
sorry i really need to understand this
so it would be side times length squared?
the problem tells us that side length = 14 area = (side length)^2 find the area
ohhhh
okay
196
it would be 196
right, (but we're not done yet though) this tells us that base = 196 now, we need to find the volume of pyramid A volume = (1/3)(base)(height) = ?
that would be 392
right. now we need to find 100*(volume of pyramid B)/(volume of pyramid A)
so i need to multiply all those numbers right?
/ means divide
then it would be 122931200 :/
volume of pyramid B/volume of pyramid A = ?
ooops
didnt see that
ok wait
800
right, 800% that's our final answer
thank you so much. i finally get it
can you help me with some other questions?
sure
Use the chart below to answer the questions: Country Population (1997 estimate) Area (square km) U.S. 272,648,000 9,364,520 Romania 22,609,000 237,391 Ghana 18,339,000 237,533 Which of these countries has the greatest population density? Which has the least? Provide an explanation and proof for your answer to receive full credit.
we have three countries, (US, Romania, and Ghana) and the table tells us the population and area of each, right? population density = population/area so, we need three values: A: population of USA/area of USA B: population of Romania/area of Romania C: population of Ghana/area of Ghana can you calculate these three values, please?
yes
wait
US is 29.115
good, keep going with the other two
Romania is 95.239
good
Ghana is 77.206
right, so Romania has the largest population density and USA has the smallest
ahhh thats it?
yeah
thanks. do have time for one more question?
sure
The coordinates A(0, 0), B(0, 3), C(4, 3) and D(4, 0) are graphed and connected together. What 3-dimensional shape will be created when this shape is rotated about the y-axis? Provide an explanation and proof for your answer to receive full credit.
you are the best thanks for helping me out
|dw:1437327503741:dw|
this gives us a rectangle when we draw out the 4 points, but when we rotate it around the y-axis like so, we get a cylinder|dw:1437327611870:dw|
|dw:1437327633016:dw| this is kinda hard to explain, but the final answer is a cylinder
okay so what formula did you use to rotate around the y axis?
haha, there isn't a formula for this one, you kinda have to use your imagination
:D
@mathstudent55 maybe you can explain? I'm really bad when it comes to explaining things like this > >
than how do i explain
@Vocaloid Excellent explanations on all three problems!
well im glad you helped me.
thank you, I'm just having a hard time explaining the whole rotating plane thing, how the rectangle becomes a cylinder
yes you are really good at explaining
When a point that is not on the y-axis is rotated about the y-axis, it creates a circle. As you rotate the rectangle about the y-axis, a cylinder with circular bases is created.
right, thank you, that's the sort of thing they're probably looking for
thank you so much mathstudent55 and Vocaloid
i appreciate your time and good explanation :)
You're welcome, but @Vocaloid is the one who deserves the thanks in this post.
how do i give you a medal mathstudent55?
You can only give one medal per post. If you already gave one to Vocaloid, then you can't give me one.
ohh sorry.

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