An open – topped box can be created by cutting squares from the four corners of a 20cm by 30cm piece of cardboard. What is the height of the box will create a volume of 1008 cm3?
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Answer:
h=3
Step-by-step explanation:
l = 30-2x
w = 20-2x
h = x
v = 1008
V=lwh
1008 = (30-2x)(20-2x)(x)
1008 = (30-2x)(20x-2x²)
1008 = 4x³-100x²+ 600x
4x³-100x²-600x-1008 = 0
4x³/4 - 100x²/4 - 600x/4-1008/4 = 0/4
(x-3)(x²-22+84) =0
x = 3 , x = 11 +√37 ,11-√37
lets take x=3
l = 30-2(3) = 24
w =20-2(3) =14
h =3