Convert 60 cubic feet to cubic inches

Question

Conversion problem

Answer 1

1ft = 12 in

1ft^3=12*12*12 in^3

so, 60 ft^3 = 60*12^3 = 103680 in^3

Answer 2

Dimensional analysis, that's what you're caught up on here.

for every 1 cubic foot you need 12in*12in*12in. If you've ever seen a 3-D cartesian coordinate system you know that you would have 3 equal lines in each direction along each axis. If you drew the grap using units of feet and were trying to draw a cubic foot, there would be three equal lines on each axis whose volume would equal l*l*l = 1ft*1ft*1ft = 1 ft³

Looking back at what i wrote above you'd have to come up with 60* 12in*12in*12in = 60 *12³ in³

There are a few ways you can tackle that multiplication, if you remember that 60 = 12*5

then you are left with 5*12*12in*12in*12in

or 5*144² in³

Just because I'm bored and don't want to use a calculator I'll show you the long way to multiply it out:

5* [(144*100)+(144*40)+(144*4)] = 5 *[14400+4000+1600+160+400+160+16] = 5*20736

5*20736 = (5*20000)+(5*700)+(5*30)+(5*6) = 100000+3500+150+30 = 1.0368*10⁵ in³