Pleasee :) Given that the total surface area of a cuboid with a square base is 66 cm and the total length value of x and of y.
of the sides is 40 cm. Find the possible volumes of the cuboid.

Total surface area = 66cm

Formula = 2x^2 + 4xy = 66cm

Given x+y= 40

y = 40 - x

Substitute

2x^2 + 4x(40 - x) = 66

2x^2 + 160x -4x^2 = 66

-2x^2 + 160x = 66

-2x^2 + 160x - 66 = 0

Factorise you get:

x =79.6 or x = 0.415

Substitute in y = 40 - x

When x = 79.6, y = 39.6 ( can’t be negative)

When x = 0.415, y = 39.6

Volume of cuboid = x (length) • x(width) • y(height)

2 possible values for volume

79.6 • 79.6 • 39.6 = 250912~

0.415 • 0.415 • 39.6 = 6.82011~