Question

medal-*Question in pic file*

Answer 1

@xapproachesinfinity can u plz help? :)

Answer 2

did you try anything?

Answer 3

no @sleepyjess

Answer 4

http://prntscr.com/6b74cn
this the wanted triangle
thinking ....

Answer 5

looks like a pyramid!

Answer 6

lol! finding the volume

Answer 7

oh i take it back it is definitely a prism

Answer 8

volume of prism

Answer 9

there is one missing puzzle
the length of the prism haha

Answer 10

the volume of the prism is Area of the base time length

Answer 11

What about integrating? Take the cross section to be perpendicular to the x-axis.

Answer 12

@DisplayError yes! can u plz show me? :)

Answer 13

oh i got it since the cross sections are square
and one side the hypotenuse of the triangle

Answer 14

so the hypotenuse is \[\sqrt{72}\]

Answer 15

kk

Answer 16

oh actually i like what Dis mention we take the cross section perpendicular to x axis
that's much better

Answer 17

so side of the square are 6
now we have got everything needed

Answer 18

so just do 1/2 6^3

Answer 19

I would solve the equation of the line \(y = -x + 6\) and take that to be one side of the cross section. Since the cross section is a square, the area of the cross section would be \(\left(-x + 6\right)^2\), then integrate that from 0 to 6.

Answer 20

hmmm
that would make the solid a pyramid not a prism

Answer 21

unless if you did what i did above
the hypotenuse to be one side of the cross section

Answer 22

but i realized that won't work
so i used what you mentioned about the cross section being perpendicular to x axis
which make it easier to solve

Answer 23

this way you have all you want
the area of the base (1/2 6^2)
the length of the prism 6

Answer 24

@DisplayError i think it would be: D, 72

Answer 25

i found 108

Answer 26

@xapproachesinfinity lol can u plz write out the steps

Answer 27

@DisplayError do u say its 108

Answer 28

everything is under you noise why are you lazy
i feel like you are not paying attention to what we are doing heheh

Answer 29

i integrated what @DisplayError

Answer 30

Integrating I get 72. But perhaps that isn't the correct procedure to solve this problem?

Answer 31

hmm you are integrating with respect to what?

Answer 32

(-x+6)^2 with upper limit 0 & lower limit 6

Answer 33

I'm assuming the cross section is perpendicular to the x-axis, so \(dx\).

Answer 34

to be honest i got -72

Answer 35

but that won't give the volume will it?

Answer 36

oh hold on

Answer 37

We're integrating \(\int \text{Area} \ dx\), so units of \(\text{length}^2 \times \text{length} = \text{length}^3\)

Answer 38

i'm not worried about the units
i'm thinking about the increment you have used

Answer 39

don't you think that if the cross section is perpendicular to x axis
we don't have \[(-x+6)^2\] or may be i'm thinking about something different here lol

Answer 40

!

Answer 41

lets skip

Answer 42

The cross sections are squares, so the area of the cross section would be given by \(\text{side}^2\). The length of one side of the square is given by \(y = -x + 6\) (assuming the cross section is perpendicular to the x-axis).

Answer 43

yeah but you made the cross section be perpendicular to x axis so you don't have that

Answer 44

i found--> http://www.math.ttu.edu/~drager/Classes/04Fall/m1352/anspract1.pdf
page 3

Answer 45

Okay, let's take the cross section to be perpendicular to the y-axis, then we have \(x = 6 - y\) and we can integrate with respect to y from y = 0 to y = 6, which would still lead to a volume of 72 cubic units.

Answer 46

thank u!!!

Answer 47

what is the deal with you mathrulezz
still doing that other problem? y=x^2, x=4 y=1?
i thought you are done with that one
the point is not to get fancy grades the point is you understand what you are doing

Answer 48

after reflecting on it i think you are right @DisplayError
i was thinking about something different in mind

Answer 49

ok

Answer 50

only 1 left

Answer 51

either A, B, or C

Answer 52

would it be: C

Answer 53

@DisplayError

Answer 54

actually D

Answer 55

hello