Answer:
x side of the square base equal to 127,20 in
h height of the cube equal to 127,20 in
Step-by-step explanation:
Volume of cube Vc is 514500 in³
Let call x side of the square base, then
Area of the base Ab = x²
Area of (4) lateral sides Al = 4 * x*h h height of the cube
Area of (4) inside partitions Ap = 4*x*h
And Vc = x²* h ⇒ 514500 = x²*h ⇒ h = 514500/ x²
Total area; At = Ab + 4 Al + 4 Ap
as Al = Ap
At = Ab + 8 Al
At = x² + 8*x*h and h = 2058000
Then area as function of x
A(x) = x² + 8*x* 514500/x² ⇒ A(x) = x² + 4116000/x
Taking derivative on both sides of the equation
A´(x) = 2x - 4116000/x² ⇒ A´(x) = 0
2x - 4116000/x² = 0
2*x³ - 4116000 = 0
x³ - 2058000 = 0
x³ = 2058000
x = 127,20 in
And h = 2058000/x² ⇒ h = 2058000/ 16179,84
h = 127,20 in
