Answer to Question #134490 in Calculus for y

Question

A rectangular box has total surface area
600 cm^2 and a square base with edge length x cm.Express the volume V of the box as a function of x. What is the volume of the box if the edge length is 5 cm?

Answer 1

Let x be the length of the side of the square base a h the height of the parallelepiped

then volume

$V=x*x*h$

S =600  total surface area

$S = 2*x^2 + 4*x*h$

$h = \frac{S-2*x^2}{4*x} = \frac{600-2*x^2}{4*x}$

$V = \frac{600-2*x^2}{4*x} *x^2 = 150*x -\frac{x^3}{2}$

for x = 5 cm V = 150*5 -125/2 = 687.5 cm³

Answer : $V = 150*x -\frac{x^3}{2}$ ; for x = 5 cm V = 150*5 -125/2 = 687.5 cm³