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.

- anonymous

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- Vocaloid

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?

- anonymous

yes

- anonymous

how can i find the area

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## More answers

- Vocaloid

area = (side length)^2

- anonymous

sorry i really need to understand this

- anonymous

so it would be side times length squared?

- Vocaloid

the problem tells us that
side length = 14
area = (side length)^2
find the area

- anonymous

ohhhh

- anonymous

okay

- anonymous

196

- anonymous

it would be 196

- Vocaloid

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) = ?

- anonymous

that would be 392

- Vocaloid

right.
now we need to find 100*(volume of pyramid B)/(volume of pyramid A)

- anonymous

so i need to multiply all those numbers right?

- Vocaloid

/ means divide

- anonymous

then it would be 122931200
:/

- Vocaloid

volume of pyramid B/volume of pyramid A = ?

- anonymous

ooops

- anonymous

didnt see that

- anonymous

ok wait

- anonymous

800

- Vocaloid

right, 800%
that's our final answer

- anonymous

thank you so much. i finally get it

- anonymous

can you help me with some other questions?

- Vocaloid

sure

- anonymous

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.

- Vocaloid

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?

- anonymous

yes

- anonymous

wait

- anonymous

US is 29.115

- Vocaloid

good, keep going with the other two

- anonymous

Romania is 95.239

- Vocaloid

good

- anonymous

Ghana is 77.206

- Vocaloid

right, so Romania has the largest population density and USA has the smallest

- anonymous

ahhh thats it?

- Vocaloid

yeah

- anonymous

thanks.
do have time for one more question?

- Vocaloid

sure

- anonymous

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.

- anonymous

you are the best thanks for helping me out

- Vocaloid

|dw:1437327503741:dw|

- Vocaloid

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|

- Vocaloid

|dw:1437327633016:dw|
this is kinda hard to explain, but the final answer is a cylinder

- anonymous

okay so what formula did you use to rotate around the y axis?

- Vocaloid

haha, there isn't a formula for this one, you kinda have to use your imagination

- anonymous

:D

- Vocaloid

@mathstudent55 maybe you can explain? I'm really bad when it comes to explaining things like this > >

- anonymous

than how do i explain

- mathstudent55

@Vocaloid Excellent explanations on all three problems!

- anonymous

well im glad you helped me.

- Vocaloid

thank you, I'm just having a hard time explaining the whole rotating plane thing, how the rectangle becomes a cylinder

- anonymous

yes you are really good at explaining

- mathstudent55

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.

- Vocaloid

right, thank you, that's the sort of thing they're probably looking for

- anonymous

thank you so much mathstudent55 and Vocaloid

- anonymous

i appreciate your time and good explanation :)

- mathstudent55

You're welcome, but @Vocaloid is the one who deserves the thanks in this post.

- anonymous

how do i give you a medal mathstudent55?

- mathstudent55

You can only give one medal per post. If you already gave one to Vocaloid, then you can't give me one.

- anonymous

ohh sorry.

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