Question

An 11-inch by 8-inch piece of cardboard has squares cut out of the corners and is folded up to make an open-top box. If the volume of the box is to be 14 cubic inches, what should be the length of the side of the cut-out corner squares?

A. No solution is possible
B. Either 3.5 inches or approximately 5.8284 inches
C. Either 3.5 inches or approximately 0.1716 inches
D. Exactly 3.5 inches

Answer 1

• Volume=14in^3

`\\ \sf{:}\implies (side)^3=14`

`\\ \sf{:}\implies side=\sqrt[3]{14}`

`\\ \sf{:}\implies side=2.5in`

Now

• L=11in
• B=8in

`\\ \sf{:}\implies Area=11(8)=88in^2`

Cut it into 10 parts as per question(Open side means five sides hence it will be 5×2=10)

`\\ \sf{:}\implies 88/10=8.8in`

Now divide by previous side

`\\ \sf{:}\implies (8.8)/(2.5)=3.52=3.5`

Option D