Question Ninet A open-top box is to be constructed from a piece of cardboard by

Question

Question Ninet A open-top box is to be constructed from a piece of cardboard by cuting congruent from the corners and the folding up the sides, The dimensions of the cardboard are shown. ? 32cm 40cm a) Express the volume of the box as a function of x b) Write an equation that represents the box with volume a) : Twice the volume of the box represented by the function in part a) ii) Haif the volume of the box represented by the function in part a) d) How are the equations in part b) related to the one in part a)? d) Use your function from part a) to determihe the values of x that will result in boxes th a volume greater that 2016 cm3 t-

Explanation / Answer

Volume = length * width * height

a. V(x) = x(40-2x)(32-2x)

b.i.

The new volume is twice of the volume we got in part a. So we get

V 1= 2x(40-2x)(32-2x)

ii .

The new volume is half of the volume we got in part a. So we will get

V2=(x/2)(40-2x)(32-2x)

x(40-2x)(32-2x)>2016

x = 10.91

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