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Question

Can someone give me an explanation on how to solve it plus the answer? There are many more q's like it so I am not really cheating...

the height of a cube is 2x cm, the width is x cm and the length is (x + 1) cm
Find the value of x, to two decimal places for which the cuboid has a volume of 8 cm 3 (cubed)

Answer 1

volume= length x width x Height
so
length=(x+1)
width=x
height=2x
volume=8 c.c.
so replace all the L,W,H, and V with appropriate equalities.
8=(x+1)(x)(2x)
combine all terms on right
8=2x^3+2x^2
simplify, setting equation equal to zero
0=2x^3+2x^2-8
graph and find x intercept so,
x=1.315

Answer 2

First it is NOT a cube
V= 2x(x+1)*x =8
2x^3+2x^2-8=0
x=1.31cm ( with two decimals)

Answer 3

volume = (2x) (x)(x+1) = 2x^3 +2x^2 =8

x^3 +x^2 -4 =0

find x

If you are familiar with analytical solutions of cubic equations , you can use those solutions

i find x to be approximately 1.315 cm

this gives

V = 1.315^3 +1.315^2 +4 =8.003 cm^3

to 2 siginificant digits, x = 1.31cm or x =1.32cm

when x =1.31cm v =7.96 cm^3
when x =1.32 cm v = 8.04 cm^3
it's your choice