Question

7. An open box is to be made from a square piece of material, 24 cm on a side, by
cutting equal squares from the corners and turning up the sides as shown (Fig.1.17).
Express the volume V of the box as a function of x.​

Answer 1

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INITIAL LENGTH OF SQUARE IS 24

AFTER CUTTING OTS CORNER BY X

THN

its lenght become 24-2x

Breath became 24-2x

height became x

volume of cuboid = function of box

v=(24-2x)(24-2x)(x)

=(24-2x)²x

=(576+4x²-96x)x

=576x-96x+4x²

V of the box is in the function of x

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Answer 2

Step-by-step explanation:

An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides.

Size of square piece = 24 * 24  cm²

Let say Size of csquare  cut from corner = x * x   cm²

Then sides of Open box would be be

24 - 2x  , 24 - 2x  & 2x

Volume of the open box = (24-2x)(24-2x)2x

= 2x(24 - 2x)²

= 2x * 2²(12 - x)²

= 8x * (x² + 144 - 24x)

= 8x³ - 192x + 1152x

V = 8x³ - 192x² + 1152x

dV/dx = 24x² - 384x + 1152

dV/dx  = 0

24x² - 384x + 1152  = 0

x² - 16x + 48 = 0

x² - 12x - 4x + 48 = 0

x(x-12) -4(x-12) = 0

(x - 4)(x-12) = 0

x = 12 is not possible as then no box will be left

x = 4 will give max volume