Question

an open box is to be made from a rectangular cardboard of side 35cm and 20cm by cutting equal square from each corner and then bending up the edges. If the base area of box thus formed is 250cm square find the length of the side of the square cut from each corner​

Answer 1

The figure for the box

Figure



The volume of the box is

V=(30−2x)(16−2x)xV=(30−2x)(16−2x)x

Simplifying the expression, we have

V=480x−92x2+4x3V=480x−92x2+4x3

Differentiating the equation with respect to xx

V′=480−184x+12x2V′=480−184x+12x2

Setting V′=0V′=0

0=480−184x+12x20=480−184x+12x2

Reducing the equation to lowest terms

0=120−46x+3x20=120−46x+3x2

Using the quadratic formula

x=−(46)±√(−46)2−4(3)(120)2(3)x=−(46)±(−46)2−4(3)(120)2(3)

x=46±262(3)x=46±262(3)

x=103,12x=103,12

Since xx cannot be 1212 because the width becomes negative, thus x=103