Question

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.

Answer 1

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?

Answer 2

yes

Answer 3

how can i find the area

Answer 4

area = (side length)^2

Answer 5

sorry i really need to understand this

Answer 6

so it would be side times length squared?

Answer 7

the problem tells us that

side length = 14
area = (side length)^2

find the area

Answer 8

ohhhh

Answer 9

okay

Answer 10

196

Answer 11

it would be 196

Answer 12

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) = ?

Answer 13

that would be 392

Answer 14

right.

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

Answer 15

so i need to multiply all those numbers right?

Answer 16

/ means divide

Answer 17

then it would be 122931200
:/

Answer 18

volume of pyramid B/volume of pyramid A = ?

Answer 19

ooops

Answer 20

didnt see that

Answer 21

ok wait

Answer 22

800

Answer 23

right, 800%

that's our final answer

Answer 24

thank you so much. i finally get it

Answer 25

can you help me with some other questions?

Answer 26

sure

Answer 27

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.

Answer 28

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?

Answer 29

yes

Answer 30

wait

Answer 31

US is 29.115

Answer 32

good, keep going with the other two

Answer 33

Romania is 95.239

Answer 34

good

Answer 35

Ghana is 77.206

Answer 36

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

Answer 37

ahhh thats it?

Answer 38

yeah

Answer 39

thanks.
do have time for one more question?

Answer 40

sure

Answer 41

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.

Answer 42

you are the best thanks for helping me out