Question

A square sheet of cardboard 100 cm by 100 cm is to have corners of side length x cut out. These cutouts will create flaps that can be folded up to form a box with no lid. The length and width of the base of the box are given by the expression (100 – 2x), and the height of the box is x, where x is in centimetres.
a) Express the volume of the box as a function of x. (2 marks)
b) Express the surface area of the box as a function of x. (2 marks)
c) What is a simplified expression for the ratio of the volume of the box to its surface area? Identify any non-permissible values of x. (2 marks)

Answer 1

The have given you everything you have to know in the description.

so since V = lxwxh
= (100-2x)(100-2x)(x)
= x(100-2x)^2

SA = base + 4 sides
= (100-2x)^2 + 4x(100-2x)
= (100-2x)[ 100-2x + 4x]
= (100-2x)(100+2x)

ratio of V/SA
= x(100-2x)/( (100-2x)(100+2x) )
= x/(100+2x) , x ≠ 50

Answer 2

Thanks,Reiny for all your help with my math!

Answer 3

welcome

Answer 4

Reiny, you were correct until the last segment of your expression for the V-SA Ratio. It is in fact...

x(100-2x)(100-2x)/(100-2x)(100+2x) And then the (100-2x) cancel formulating

V/SA= x(100-2x) / (100+2x)