Question

WILL MEDAL AND FAN
The volume of a square based pyramid is eighty-one cubic meters. What is the volume of the cube with the same side length and height

Answer 1

3*81

Answer 2

is 243

Answer 3

a cube with side length s has a volume of s^3

a pyramid with the same side length base is (1/3)s^3...

pyramids are always 1/3 the volume of their corresponding prisms...

Answer 4

that goes for cones and cylinders as well...

Answer 5

so what is the equation i must do?

Answer 6

Wait, is the answer 243

Answer 7

:) yes...the answer is 243 cubic meters

Answer 8

m squared

Answer 9

m cubed...volume.

Answer 10

thank you, iwill medal and fan you

Answer 11

do you think you can help me with one more

Answer 12

i can give it my best shot

Answer 13

What is the new volume of a rectangular prism that is originally twelve cubic meters and is then resized using a scale factor of 3 on each side length

Answer 14

so a rectangular prism has a volume formula of
\[V=lwh\]
so if each of these goes up by a factor of 3, your new formula would be
\[(3l)(3w)(3h) = (3)(3)(3)(lwh)\]

Answer 15

if your original prism (lwh) was 12, what would the new volume be?

Answer 16

i believe the answer is 36m

Answer 17

not quite...each of the sides was made bigger by a factor of 3.

notice i have 3 times 3 times 3 in my post?

Answer 18

well 3*3*3 is 27.. so what do i do from here

Answer 19

you see in my post where i have
\[(3)(3)(3)(lwh)\]
(lwh) is the vloume from your original prism...multiplying it by the (3)(3)(3) is the volume of the *new* prism...

Answer 20

Yes, increasing lengths by factor k increases areas by k^2 and volumes by k^3.

Answer 21

would this answer be around 110? my calculations are a little off

Answer 22

no...that's way off...tell me what calculations you are doing...

Answer 23

im sorry, im not very good if its not multiple choice

Answer 24

that's ok...we can get you there...tell me how you came up with 110 so i can see where the disconnect is.

Answer 25

i did meant 100, i did 27*3 and got 81, so i rounded to the nearest hundredth and asked if it was near there

Answer 26

show the choices u have

Answer 27

it is not multiple choice

Answer 28

oh

Answer 29

ok...let's take a step back.

your original prism had a length, a width and a height...and the volume, we know, is 12

with me so far?

Answer 30

yes

Answer 31

now we don't know the l, w, and h...and frankly, we don't care.

what we *do* know is that we have another prism and this one has a length, width and height each 3 times the original prism.

still tracking?

Answer 32

i believe so

Answer 33

lol...good enough for now.

what we need to figure out is what is the volume of the *new* prism.

so let's look at the formula for a rectangular prism...

\[V=lwh\]

simple enough, right?

Answer 34

yes

Answer 35

so our original prism had sides l, w, and h and V=12
\[12=lwh\]

and we know that the new prism has sides (so we don't confuse with the first one) x, y, and z where
x=3l
y=3w
z=3h

do you see where i get that? this is the crucial piece...

Answer 36

i understand this part now.

Answer 37

good :)

so using the same volume formula the new prism would have
\[V=xyz=(3l)(3w)(3h)=(3)(3)(3)(lwh)\]

Answer 38

if we plug 12 in for lwh (since that is the volume of the original prism) we would have the volume of the new one, yes?

Answer 39

324!!!

Answer 40

perfect!

Answer 41

Thank you so much

Answer 42

and i have fanned you

Answer 43

you're quite welcome...i told you we would get you there

Answer 44

Yup, have a good day

Answer 45

you too