Question

A closed box in the shape of a cuboid has dimensions x cm, y cm and 5 cm.
The volume of the box is 40 cm^3 and the external surface area is 76 cm^2.

A) use the information about the volume to find and equation connecting x and y

B) use the information about the external surface area to find another equation connecting x and y.

C) solve the equations simultaneously.

I just need help with part A and B.

Thank you.
:)

Answer 1

A) since V = lwh
5xy = 40
xy = 8 or y = 8/x

B)
surface area = 2xy + 2(5x) + 2(5y) = 76
xy + 5x + 5y = 38
x(8/x) + 5x + 5(8/x) = 38
8 + 5x + 40/x = 38
5x + 40/x = 30


C)
times x
5x^2 - 30x + 40 = 0
x^2 - 6x + 8 = 0
(x-4)(x-2) = 0
x = 4 or x= 2

if x=4, y=2
if x=2, y=4

or we can just say the base is 4 by 2