- #1

Physicsnoob90

- 51

- 0

## Homework Statement

The length ℓ, width

*w*, and height

*h*of a box change with time. At a certain instant the dimensions are ℓ = 4 m and

w = h = 9 m, and ℓ and

*w*are increasing at a rate of 1 m/s while

*h*is decreasing at a rate of 6 m/s. At that instant find the rates at which the following quantities are changing.

(A) The Volume

(B) The Surface Area

(C) the length of a diagonal (round two decimals places)

## Homework Equations

The Chain rule, Partial Derivative

## The Attempt at a Solution

I already found A (ans: -99 m^3/s) and B (ans: -94 m^2/s)

for C:

1. i differentiated the formula L^2= ℓ^2+w^2+h^2 to 2L(dL/dt) = 2ℓ(dℓ/dt) + 2w(dw/dt) + 2h (dh/dt)

2. let dℓ/dt = dw/dt = 1 m/s and dh/dt = -6 m/s

3. my answer came as 2L(dL/dt) = 82 but I'm completely lost after this part