what will happen to the volume of a rectangular prism when the length and width are doubled and the height is tripled

Question

jhannybean · Answer

Volume is directly proportional to the width, height and length of a rectangular prism, so as those increase, Volume will increase as well. $$V=whl$$$$\uparrow V \rightarrow  ~\uparrow (whl)$$

anonymous · Answer

Thanks but will the volume be tripled? or doubled?

jim_thompson5910 · Answer

Let's say we had a prism with these dimensions

Length: L = 8
Width: W = 5
Height: H = 12

what is the volume of this prism?

anonymous · Answer

that would be 480 units

jim_thompson5910 · Answer

correct

jim_thompson5910 · Answer

480 cubic units actually

jim_thompson5910 · Answer

"the length and width are doubled and the height is tripled"

so take the original dimensions

L = 8
W = 5
H = 12

double the length and width
L = 8 ---> L = 16
W = 5---> W = 10

triple the height
H = 12 ---> H = 36

We now have this new prism

L = 16
W = 10
H = 36

the volume of this new prism is what?

anonymous · Answer

5760 m3

jim_thompson5910 · Answer

old volume = 480 cubic units
new volume = 5760 cubic units

divide the new volume by the old volume

jim_thompson5910 · Answer

(new volume)/(old volume) = ???

anonymous · Answer

12

jim_thompson5910 · Answer

correct

jim_thompson5910 · Answer

so the new volume is 12 times bigger than the old volume

jim_thompson5910 · Answer

notice how 2*2*3 = 12

so you can just multiply out those transformations to get the answer

anonymous · Answer

ok thanks!

jim_thompson5910 · Answer

you're welcome