Question

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 17 in. by 10 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume.\

Answer 1

Answer: 156.03 in³

Step-by-step explanation:

Card board length= 17 in

Cardboard width= 10 in

Now, after cutting the length becomes= 17-2x

Width becomes= 10-2x

Let the height be= x

So Volume= (17-2x) * (10-2x) * x

V= (17-2x) * (10-2x) * x

Taking derivative wrt 'x' on both sides

$\frac{dV}{dx}$= $\frac{d}{dx}$ [ (17-2x) * (10-2x) * x]

Put $\frac{dV}{dx}$ and solving we get

12x²- 108x+ 170=0

Solving quadratic equation, we get

x= 6.96 and x= 2.03

Put x=6.96

V= -84.03 (not possible)

Put x= 2.03

V= 156.03 in³