Thread: V and SA of rectangular Box

Write an expression for the volume and surface are of a rectangular box if

w=x+2
l=2x+5
h=x+4

Originally Posted by william

Write an expression for the volume and surface are of a rectangular box if

w=x+2
l=2x+5
h=x+4

V = lwh = ....

S = 2(wl) + 2(hl) + 2(wh) = ..... (assuming the box is not open at the top)

Originally Posted by mr fantastic

V = lwh = ....

S = 2(wl) + 2(hl) + 2(wh) = ..... (assuming the box is not open at the top)

V=(2x+5)(x+2)(x+4) how would I simplify this?

SA= 2(2x+5)(x+2)+2(2x+5)(x+4)+2(x+2)(x+4)
=(4x+10)(x+2)+(4x+10)(x+4)+(2x+4)(x+4)
=4x^2+4x^2+2x^2+8x+10x+16x+10x+8x+4x+20+40+16
=10x^2+56x+76, correct?

Originally Posted by william

V=(2x+5)(x+2)(x+4) how would I simplify this? Mr F says: Why expand? It's fine like that.

SA= 2(2x+5)(x+2)+2(2x+5)(x+4)+2(x+2)(x+4)
=(4x+10)(x+2)+(4x+10)(x+4)+(2x+4)(x+4)
=4x^2+4x^2+2x^2+8x+10x+16x+10x+8x+4x+20+40+16
=10x^2+56x+76, correct?

I substituted x = 1 and your SA gave the correct answer so it's probably OK (I don't check algebra that's this tedious - I always make mistakes from boredom).

Originally Posted by mr fantastic

I substituted x = 1 and your SA gave the correct answer so it's probably OK (I don't check algebra that's this tedious - I always make mistakes from boredom).

Alright, thanks.

Do you have any input on how to get the expression for the volume.
I am unsure how to expand and simplify (2x+5)(x+2)(x+4)
I see you have written that it is unnecessary and i do take your word for it, although how would I if i wanted to?

Originally Posted by william

Alright, thanks.

Do you have any input on how to get the expression for the volume.
I am unsure how to expand and simplify (2x+5)(x+2)(x+4)
I see you have written that it is unnecessary and i do take your word for it, although how would I if i wanted to?

First expand (2x + 5)(x + 2): 2x^2 + 9x + 10.

Now expand (2x^2 + 9x + 10)(x + 4).