If the volume of a cube is increasing at a rate of 24 in^3 per min.?

Question

and the edge of the cube is increasing at 2 in/min. What is the length of each edge of the cube?
A) 2 in
B) 2√(2) in
C) ³√(12) in
D) 4 in
E) 8 in

Answer 1

V = s³

Differentiate:

V' = 3s² s'

Substitute 24 for V' and 2 for s':

24 = 3s²(2)

Divide both sides by 6:

s² = 4

Take square root:

s = 2

Answer 2

You probably already realize this problem needs to be solved using derivation. You are given:

dV/dt =24 in^3/min (V = volume)
dL/dt = 2 in/min (L = length)

The formula for cube is: V = L^3
Take the derivative of both sides with respect to time, and you end up with:

dV/dt = 3L^2 x dL/dt

Now, put in the given numbers.

24 = 3L^2 x 2
12 = 3L^2
4 = L^2
L = 2

Therefore, the length of each side is 2 inches.

Answer 3

WTF?

When the hell would a cube expand